1. CJM Online first
 Stokke, Ross Thomas

Fourier spaces and completely isometric representations of Arens product algebras
Motivated by the definition of a semigroup
compactification of a locally compact group and a large collection
of examples, we introduce the notion of an (operator) ``homogeneous
left dual Banach algebra" (HLDBA) over a (completely contractive)
Banach algebra $A$. We prove a Gelfandtype representation
theorem showing that every HLDBA over $A$ has a concrete realization
as an (operator) homogeneous left Arens product algebra: the
dual of a subspace of $A^*$ with a compatible (matrix) norm and
a type of left Arens product ${\scriptstyle\square}$. Examples include all left
Arens product algebras over $A$, but also  when $A$ is the
group algebra of a locally compact group  the dual of its Fourier
algebra. Beginning with any (completely) contractive (operator)
$A$module action $Q$ on a space $X$, we introduce the (operator)
Fourier space $(\mathcal F_Q(A^*), \ \cdot \_Q)$ and
prove that
$(\mathcal F_Q(A^*)^*, {\scriptstyle\square})$ is the unique (operator) HLDBA over
$A$ for which there is a weak$^*$continuous completely isometric
representation as completely bounded operators on $X^*$ extending
the dual module representation.
Applying our theory to several examples of (completely contractive)
Banach algebras $A$ and module operations, we provide new characterizations
of
familiar HLDBAs over $A$ and we recover  and often extend
 some
(completely) isometric representation theorems concerning
these HLDBAs.
Keywords:Banach algebra, operator space, Arens product, group algebra, Fourier algebra Categories:47L10, 43A20, 43A30, 46H15, 46H25, 47L25 

2. CJM Online first
 Cameron, Jan; Smith, Roger R.

A Galois correspondence for reduced crossed products of unital simple C$^*$algebras by discrete groups
Let a discrete group $G$ act on a unital simple C$^*$algebra
$A$ by outer automorphisms. We establish a Galois correspondence
$H\mapsto A\rtimes_{\alpha,r}H$ between subgroups of $G$ and
C$^*$algebras $B$ satisfying $A\subseteq B \subseteq A\rtimes_{\alpha,r}G$,
where
$A\rtimes_{\alpha,r}G$ denotes the reduced crossed product. For
a twisted dynamical system $(A,G,\alpha,\sigma)$, we also prove
the corresponding result for the reduced twisted crossed product
$A\rtimes^\sigma_{\alpha,r}G$.
Keywords:C$^*$algebra, group, crossed product, bimodule, reduced, twisted Categories:46L55, 46L40 

3. CJM Online first
 Georgescu, Magdalena Cecilia

Integral Formula for Spectral Flow for $p$Summable Operators
Fix a von Neumann algebra $\mathcal{N}$ equipped with a suitable trace
$\tau$. For a path of selfadjoint BreuerFredholm operators, the
spectral flow measures the net amount of spectrum which moves from
negative to nonnegative. We consider specifically the case of paths
of bounded perturbations of a fixed unbounded selfadjoint
BreuerFredholm operator affiliated with $\mathcal{N}$. If the unbounded
operator is psummable (that is, its resolvents are contained in the
ideal $L^p$), then it is possible to obtain an integral formula which
calculates spectral flow. This integral formula was first proven by
Carey and Phillips, building on earlier approaches of Phillips. Their
proof was based on first obtaining a formula for the larger class of
$\theta$summable operators, and then using Laplace transforms to
obtain a psummable formula. In this paper, we present a direct proof
of the psummable formula, which is both shorter and simpler than
theirs.
Keywords:spectral flow, $p$summable Fredholm module Categories:19k56, 46L87, , 58B34 

4. CJM Online first
 Glöckner, Helge

Completeness of infinitedimensional Lie groups in their left uniformity
We prove completeness for the main examples
of infinitedimensional Lie groups and some related topological
groups.
Consider a sequence
$G_1\subseteq G_2\subseteq\cdots$ of topological groups~$G_n$
such that~$G_n$ is a subgroup of $G_{n+1}$ and the latter induces
the given topology on~$G_n$,
for each $n\in\mathbb{N}$.
Let $G$ be the direct limit of the sequence in the category of
topological groups.
We show that $G$ induces the given topology on each~$G_n$ whenever
$\bigcup_{n\in \mathbb{N}}V_1V_2\cdots V_n$ is an identity neighbourhood
in~$G$
for all identity neighbourhoods $V_n\subseteq G_n$. If, moreover,
each $G_n$ is complete, then~$G$ is complete.
We also show that the weak direct product $\bigoplus_{j\in J}G_j$
is complete for
each family $(G_j)_{j\in J}$ of complete Lie groups~$G_j$.
As a consequence, every strict direct limit $G=\bigcup_{n\in
\mathbb{N}}G_n$ of finitedimensional
Lie groups is complete, as well as the diffeomorphism group
$\operatorname{Diff}_c(M)$
of a paracompact finitedimensional smooth manifold~$M$
and the test function group $C^k_c(M,H)$, for each $k\in\mathbb{N}_0\cup\{\infty\}$
and complete Lie group~$H$
modelled on a complete locally convex space.
Keywords:infinitedimensional Lie group, left uniform structure, completeness Categories:22E65, 22A05, 22E67, 46A13, 46M40, 58D05 

5. CJM Online first
 Wang, Xing; Zhang, Chunjie

Pointwise convergence of solutions to the SchrÃ¶dinger equation on manifolds
Let $(M^n,g)$ be a Riemannian manifold without
boundary. We study the amount of initial regularity is required
so that the solution to free SchrÃ¶dinger equation converges
pointwise to its initial data. Assume the initial data is in
$H^\alpha(M)$. For Hyperbolic Space, standard Sphere and the
2 dimensional Torus, we prove that $\alpha\gt \frac{1}{2}$ is enough.
For general compact manifolds, due to lacking of local smoothing
effect, it is hard to beat the bound $\alpha\gt 1$ from interpolation.
We managed to go below 1 for dimension $\leq 3$. The more interesting
thing is that, for 1 dimensional compact manifold, $\alpha\gt \frac{1}{3}$
is sufficient.
Keywords:pointwise convergence, SchrÃ¶dinger operator, manifold, Strichartz estimate Categories:35L05, 46E35, 42B37 

6. CJM Online first
 Mingo, James A.; Popa, Mihai

Freeness and The Partial Transposes of Wishart Random Matrices
We show that the partial transposes of complex Wishart
random matrices are asymptotically free. We also investigate
regimes where the number of blocks is fixed but the size of
the blocks increases. This gives a example where the partial
transpose produces freeness at the operator level. Finally
we investigate the case of real Wishart matrices.
Keywords:free probability, random matrix, partial transpose, quantum information theory Categories:15B52, 46L54, 60B20 

7. CJM Online first
 Astashkin, Sergey V.; Lesnik, Karol; Maligranda, Lech

Isomorphic structure of CesÃ ro and Tandori spaces
We investigate the isomorphic structure of the CesÃ ro spaces
and their duals, the Tandori spaces.
The main result states that the CesÃ ro function space $Ces_{\infty}$
and its sequence counterpart
$ces_{\infty}$ are isomorphic, which answers the question posted
previously.
This is rather surprising
since $Ces_{\infty}$ (like the known Talagrand's example)
has no natural lattice predual.
We prove that $ces_{\infty}$ is not isomorphic to ${\ell}_{\infty}$
nor is $Ces_{\infty}$ isomorphic to the
Tandori space $\widetilde{L_1}$ with the norm $\f\_{\widetilde{L_1}}=
\\widetilde{f}\_{L_1},$ where
$\widetilde{f}(t):= \operatorname{esssup}_{s \geq t} f(s).$ Our investigation
involves also an examination of the
Schur and DunfordPettis properties of CesÃ ro and Tandori
spaces.
In particular, using results of Bourgain we show that a wide
class of CesÃ roMarcinkiewicz and
CesÃ roLorentz spaces have the latter property.
Keywords:CesÃ ro and Tandori sequence spaces, CesÃ ro and Tandori function spaces, CesÃ ro operator, Banach ideal space, symmetric space, Schur property, DunfordPettis property, isomorphism Categories:46E30, 46B20, 46B42, 46B45 

8. CJM Online first
 Matsumoto, Kengo

Asymptotic continuous orbit equivalence of Smale spaces and Ruelle algebras
In the first part of the paper, we introduce notions of
asymptotic continuous orbit equivalence
and asymptotic conjugacy in Smale spaces
and characterize them in terms of their asymptotic Ruelle algebras
with their dual actions.
In the second part, we introduce a groupoid $C^*$algebra which
is an extended version
of the asymptotic Ruelle algebra from a Smale space
and study the extended Ruelle algebras from the view points of
CuntzKrieger algebras.
As a result, the asymptotic Ruelle algebra is realized as a fixed
point algebra
of the extended Ruelle algebra under certain circle action.
Keywords:hyperbolic dynamics, Smale space, Ruelle algebra, groupoid, zeta function, continuous orbit equivalence, shifts of finite type, CuntzKrieger algebra Categories:37D20, 46L35 

9. CJM 2018 (vol 70 pp. 1236)
 Clouâtre, Raphaël

Unperforated Pairs of Operator Spaces and Hyperrigidity of Operator Systems
We study restriction and extension properties for states on C$^*$algebras
with an eye towards hyperrigidity of operator systems. We use
these ideas to provide supporting evidence for Arveson's hyperrigidity
conjecture. Prompted by various characterizations of hyperrigidity
in terms of states, we examine unperforated pairs of selfadjoint
subspaces in a C$^*$algebra. The configuration of the subspaces
forming an unperforated pair is in some sense compatible with
the order structure of the ambient C$^*$algebra. We prove
that commuting pairs are unperforated, and obtain consequences
for hyperrigidity. Finally, by exploiting recent advances in
the tensor theory of operator systems, we show how the weak expectation
property can serve as a flexible relaxation of the notion of
unperforated pairs.
Keywords:operator system, state, peak point, hyperrigidity conjecture Categories:46L07, 46L30, 46L52 

10. CJM 2018 (vol 70 pp. 1261)
 Fricain, Emmanuel; Hartmann, Andreas; Ross, William T.

Range Spaces of Coanalytic Toeplitz Operators
In this paper we discuss the range of a coanalytic Toeplitz
operator. These range spaces are closely related to de BrangesRovnyak
spaces (in some cases they are equal as sets). In order to understand
its structure, we explore when
the range space decomposes into the range of an associated analytic
Toeplitz operator and an identifiable orthogonal complement.
For certain cases, we compute this orthogonal complement in terms
of the kernel of a certain Toeplitz operator on the Hardy space
where we focus on when this kernel is a model space (backward
shift invariant subspace).
In the spirit of AhernClark, we also discuss the nontangential
boundary behavior in these range spaces. These results give us
further insight into the description of the range of a coanalytic
Toeplitz operator as well as its orthogonal decomposition. Our
AhernClark type results, which are stated in a general abstract
setting, will also have applications to related subHardy Hilbert
spaces of analytic functions such as the de BrangesRovnyak spaces
and the harmonically weighted Dirichlet spaces.
Keywords:Toeplitz operator, Hardy space, range space, de BrangesRovnyak space, boundary behavior, kernel function, nonextreme point, corona pair Categories:30J05, 30H10, 46E22 

11. CJM 2018 (vol 70 pp. 1008)
 Elazar, Boaz; Shaviv, Ary

Schwartz Functions on Real Algebraic Varieties
We define Schwartz functions, tempered functions and tempered
distributions on (possibly singular) real algebraic varieties.
We prove that all classical properties of these spaces, defined
previously on affine spaces and on Nash manifolds, also hold
in the case of affine real algebraic varieties, and give partial
results for the nonaffine case.
Keywords:real algebraic geometry, Schwartz function, tempered distribution Categories:14P99, 14P05, 22E45, 46A11, 46F05 

12. CJM 2017 (vol 70 pp. 400)
 Osaka, Hiroyuki; Teruya, Tamotsu

The JiangSu absorption for inclusions of unital C*algebras
We introduce the tracial Rokhlin property for a conditional expectation
for an inclusion
of unital C*algebras $P \subset A$ with index finite, and show
that an action $\alpha$
from a finite group $G$ on a simple unital C*algebra $A$ has
the tracial Rokhlin property
in the sense of N. C. Phillips
if and only if the canonical conditional expectation $E\colon
A \rightarrow A^G$ has the tracial
Rokhlin property.
Let $\mathcal{C}$ be a class of infinite dimensional stably
finite separable unital C*algebras
which is closed under the following conditions:
(1)
If $A \in {\mathcal C}$ and $B \cong A$, then $B \in \mathcal{C}$.
(2)
If $A \in \mathcal{C}$ and $n \in \mathbb{N}$, then $M_n(A) \in \mathcal{C}$.
(3)
If $A \in \mathcal{C}$ and $p \in A$ is a nonzero projection,
then $pAp \in \mathcal{C}$.
Suppose that any C*algebra in $\mathcal{C}$ is weakly semiprojective.
We prove that if $A$ is a local tracial $\mathcal{C}$algebra
in the sense of Fan and Fang and a conditional expectation
$E\colon A \rightarrow P$ is of indexfinite type with the tracial
Rokhlin property, then $P$ is a unital
local tracial $\mathcal{C}$algebra.
The main result is that if $A$ is simple, separable, unital
nuclear, JiangSu absorbing
and $E\colon A \rightarrow P$ has the tracial Rokhlin property,
then $P$ is JiangSu absorbing.
As an application, when an action $\alpha$
from a finite group $G$ on a simple unital C*algebra $A$ has
the tracial Rokhlin property,
then for any subgroup $H$ of $G$ the fixed point algebra $A^H$
and the crossed product algebra
$A \rtimes_{\alpha_{H}} H$ is JiangSu absorbing.
We also show that the strict comparison property for a Cuntz
semigroup $W(A)$
is hereditary to $W(P)$ if $A$ is simple, separable, exact,
unital,
and $E\colon A \rightarrow P$ has the tracial Rokhlin property.
Keywords:JiangSu absorption, inclusion of C*algebra, strict comparison Categories:46L55, 46L35 

13. CJM Online first
 Courtney, Kristin; Shulman, Tatiana

Elements of $C^*$algebras attaining their norm in a finitedimensional representation
We characterize the class of RFD $C^*$algebras as those containing
a dense subset of elements that attain their norm under a finitedimensional
representation. We show further that this subset is the whole
space precisely when every irreducible representation of the
$C^*$algebra is finitedimensional, which is equivalent to the
$C^*$algebra having no simple infinitedimensional AF subquotient.
We apply techniques from this proof to show the existence of
elements in more general classes of $C^*$algebras whose norms
in finitedimensional representations fit certain prescribed
properties.
Keywords:AFtelescope, RFD, projective Categories:46L05, 47A67 

14. CJM Online first
 Li, Hui; Yang, Dilian

Boundary quotient C*algebras of products of odometers
In this paper, we study the boundary quotient C*algebras associated
to products of odometers. One of our main results
shows that the boundary quotient C*algebra of the standard product
of $k$ odometers
over $n_i$letter alphabets ($1\le i\le k$) is always nuclear,
and that
it is a UCT Kirchberg algebra
if and only if $\{\ln n_i: 1\le i\le k\}$ is rationally independent,
if and only if the associated singlevertex $k$graph C*algebra
is simple.
To achieve this, one of our main steps is to construct a topological
$k$graph such that
its associated CuntzPimsner C*algebra is isomorphic to the
boundary quotient C*algebra.
Some relations between the boundary quotient C*algebra and the
C*algebra $\mathrm{Q}_\mathbb{N}$ introduced by Cuntz are also
investigated.
Keywords:C*algebra; semigroup; odometer; topological $k$graph; product system; ZappaSzÃ©p product Category:46L05 

15. CJM 2017 (vol 70 pp. 3)
 BenaychGeorges, Florent; Cébron, Guillaume; Rochet, Jean

Fluctuation of matrix entries and application to outliers of elliptic matrices
For any family of $N\times N$ random matrices $(\mathbf{A}_k)_{k\in
K}$ which is invariant, in law, under unitary conjugation, we
give general sufficient conditions for central limit theorems
for random variables of the type $\operatorname{Tr}(\mathbf{A}_k
\mathbf{M})$, where the matrix $\mathbf{M}$ is deterministic
(such random variables include for example the normalized matrix
entries of the $\mathbf{A}_k$'s). A consequence is the asymptotic
independence of the projection of the matrices $\mathbf{A}_k$
onto the subspace of null trace matrices from their projections
onto the orthogonal of this subspace. These results are used
to study the asymptotic behavior of the outliers of a spiked
elliptic random matrix. More precisely, we show that the fluctuations
of these outliers around their limits can have various rates
of convergence, depending on the Jordan Canonical Form of the
additive perturbation. Also, some correlations can arise between
outliers at a macroscopic distance from each other. These phenomena
have already been observed
with random matrices
from the Single Ring Theorem.
Keywords:random matrix, Gaussian fluctuation, spiked model, elliptic random matrix, Weingarten calculus, Haar measure Categories:60B20, 15B52, 60F05, 46L54 

16. CJM Online first
 Handelman, David

Nearly approximate transitivity (AT) for circulant matrices
By previous work of Giordano and the author, ergodic
actions of $\mathbf Z$ (and other discrete groups) are completely classified
measuretheoretically by their dimension space, a construction
analogous to the dimension group used in C*algebras and topological
dynamics. Here we investigate how far from AT (approximately
transitive) can actions be which derive from circulant (and related)
matrices. It turns out not very: although nonAT actions can
arise from this method of construction, under very modest additional
conditions, ATness arises; in addition, if we drop the positivity
requirement in the isomorphism of dimension spaces, then all
these ergodic actions satisfy an analogue of AT. Many examples
are provided.
Keywords:approximately transitive, ergodic transformation, circulant matrix, hemicirculant matrix, dimension space, matrixvalued random walk Categories:37A05, 06F25, 28D05, 46B40, 60G50 

17. CJM 2017 (vol 70 pp. 294)
 Eilers, Søren; Restorff, Gunnar; Ruiz, Efren; Sørensen, Adam P. W.

Geometric classification of graph C*algebras over finite graphs
We address the classification problem for graph $C^*$algebras of
finite graphs (finitely many edges and vertices), containing
the class of CuntzKrieger algebras as a
prominent special case. Contrasting earlier work, we do not assume
that the graphs satisfy the standard condition (K), so that the
graph
$C^*$algebras may come with uncountably many ideals.
We find that in this generality, stable isomorphism of graph
$C^*$algebras does not coincide with the geometric notion of Cuntz
move equivalence. However, adding a modest condition on the
graphs, the two notions are proved to be mutually equivalent and
equivalent to the $C^*$algebras having isomorphic $K$theories. This
proves in turn that under this condition, the graph
$C^*$algebras are in fact classifiable by $K$theory, providing in
particular complete classification when the $C^*$algebras in question
are either of real rank zero or type I/postliminal. The key ingredient
in obtaining these results is a characterization of Cuntz move
equivalence using the adjacency matrices of the graphs.
Our results are applied to discuss the classification problem
for the quantum lens spaces defined by Hong and SzymaÅski,
and to complete the classification of graph $C^*$algebras associated to
all simple graphs with four vertices or less.
Keywords:graph $C^*$algebra, geometric classification, $K$theory, flow equivalence Categories:46L35, 46L80, 46L55, 37B10 

18. CJM 2017 (vol 69 pp. 1385)
 Pasnicu, Cornel; Phillips, N. Christopher

The Weak Ideal Property and Topological Dimension Zero
Following up on previous work,
we prove a number of results for C*algebras
with the weak ideal property
or topological dimension zero,
and some results for C*algebras with related properties.
Some of the more important results include:
$\bullet$
The weak ideal property
implies topological dimension zero.
$\bullet$
For a separable C*algebra~$A$,
topological dimension zero is equivalent to
${\operatorname{RR}} ({\mathcal{O}}_2 \otimes A) = 0$,
to $D \otimes A$ having the ideal property
for some (or any) Kirchberg algebra~$D$,
and to $A$ being residually hereditarily in
the class of all C*algebras $B$ such that
${\mathcal{O}}_{\infty} \otimes B$
contains a nonzero projection.
$\bullet$
Extending the known result for ${\mathbb{Z}}_2$,
the classes of C*algebras
with residual (SP),
which are residually hereditarily (properly) infinite,
or which are purely infinite and have the ideal property,
are closed under crossed products by arbitrary actions
of abelian $2$groups.
$\bullet$
If $A$ and $B$ are separable,
one of them is exact,
$A$ has the ideal property,
and $B$ has the weak ideal property,
then $A \otimes_{\mathrm{min}} B$ has the weak ideal property.
$\bullet$
If $X$ is a totally disconnected locally compact Hausdorff space
and $A$ is a $C_0 (X)$algebra
all of whose fibers have one of the weak ideal property,
topological dimension zero,
residual (SP),
or the combination of pure infiniteness and the ideal property,
then $A$ also has the corresponding property
(for topological dimension zero, provided $A$ is separable).
$\bullet$
Topological dimension zero,
the weak ideal property,
and the ideal property
are all equivalent
for a substantial class of separable C*algebras including
all separable locally AH~algebras.
$\bullet$
The weak ideal property does not imply the ideal property
for separable $Z$stable C*algebras.
We give other related results,
as well as counterexamples to several other statements
one might hope for.
Keywords:ideal property, weak ideal property, topological dimension zero, $C_0 (X)$algebra, purely infinite C*algebra Category:46L05 

19. CJM 2017 (vol 70 pp. 53)
 Dantas, Sheldon; García, Domingo; Maestre, Manuel; Martín, Miguel

The BishopPhelpsBollobÃ¡s property for compact operators
We study the BishopPhelpsBollobÃ¡s property (BPBp for short)
for compact operators. We present some abstract techniques which
allows to carry the BPBp for compact operators from sequence
spaces to function spaces. As main applications, we prove the
following results. Let $X$, $Y$ be Banach spaces. If $(c_0,Y)$
has the BPBp for compact operators, then so do $(C_0(L),Y)$ for
every locally compact Hausdorff topological space $L$ and $(X,Y)$
whenever $X^*$ is isometrically isomorphic to $\ell_1$.
If $X^*$ has the RadonNikodÃ½m property and $(\ell_1(X),Y)$
has the BPBp for compact operators, then so does $(L_1(\mu,X),Y)$
for every positive measure $\mu$; as a consequence, $(L_1(\mu,X),Y)$
has the the BPBp for compact operators when $X$ and $Y$ are finitedimensional
or $Y$ is a Hilbert space and $X=c_0$ or $X=L_p(\nu)$ for any
positive measure $\nu$ and $1\lt p\lt \infty$.
For $1\leq p \lt \infty$, if $(X,\ell_p(Y))$ has the BPBp for compact
operators, then so does $(X,L_p(\mu,Y))$ for every positive measure
$\mu$ such that $L_1(\mu)$ is infinitedimensional. If $(X,Y)$
has the BPBp for compact operators, then so do $(X,L_\infty(\mu,Y))$
for every $\sigma$finite positive measure $\mu$ and $(X,C(K,Y))$
for every compact Hausdorff topological space $K$.
Keywords:BishopPhelps theorem, BishopPhelpsBollobÃ¡s property, norm attaining operator, compact operator Categories:46B04, 46B20, 46B28, 46B25, 46E40 

20. CJM 2017 (vol 70 pp. 26)
 Bosa, Joan; Petzka, Henning

Comparison Properties of the Cuntz semigroup and applications to C*algebras
We study comparison properties in the category $\mathrm{Cu}$ aiming to
lift results to the C*algebraic setting. We introduce a new
comparison property and relate it to both the CFP and $\omega$comparison.
We show differences of all properties by providing examples,
which suggest that the corona factorization for C*algebras might
allow for both finite and infinite projections. In addition,
we show that R{\o}rdam's simple, nuclear C*algebra with a finite
and an infinite projection does not have the CFP.
Keywords:classification of C*algebras, cuntz semigroup Categories:46L35, 06F05, 46L05, 19K14 

21. CJM 2017 (vol 70 pp. 721)
 Bao, Guanlong; Göğüş, Nihat Gökhan; Pouliasis, Stamatis

On Dirichlet Spaces with a Class of Superharmonic Weights
In this paper, we investigate Dirichlet spaces $\mathcal{D}_\mu$ with
superharmonic weights induced by positive Borel measures $\mu$
on
the open unit disk. We establish the AlexanderTaylorUllman
inequality for $\mathcal{D}_\mu$ spaces and we characterize the cases where
equality occurs.
We define a class of weighted Hardy spaces $H_{\mu}^{2}$ via
the balayage of the measure $\mu$.
We show that $\mathcal{D}_\mu$
is equal to $H_{\mu}^{2}$ if and only if $\mu$ is a
Carleson measure for $\mathcal{D}_\mu$. As an application, we obtain the
reproducing kernel of $\mathcal{D}_\mu$ when $\mu$ is an infinite
sum of point mass measures. We consider the boundary
behavior and innerouter factorization of functions in $\mathcal{D}_\mu$.
We also characterize the boundedness and
compactness of composition operators on $\mathcal{D}_\mu$.
Keywords:Dirichlet space, Hardy space, superharmonic weight Categories:30H10, 31C25, 46E15 

22. CJM 2017 (vol 69 pp. 1312)
 Fricain, Emmanuel; Rupam, Rishika

On Asymptotically Orthonormal Sequences
An asymptotically orthonormal sequence is a sequence which is
"nearly" orthonormal in the sense that it satisfies the Parseval
equality up to two constants close to one. In this paper, we
explore such sequences formed by normalized reproducing kernels
for model spaces and de BrangesRovnyak spaces.
Keywords:function space, de BrangesRovnyak and model space, reproducing kernel, asymptotically orthonormal sequence Categories:30J05, 30H10, 46E22 

23. CJM 2017 (vol 70 pp. 804)
 Giannopoulos, Apostolos; Koldobsky, Alexander; Valettas, Petros

Inequalities for the Surface Area of Projections of Convex Bodies
We provide general inequalities that compare the surface area
$S(K)$ of a convex body $K$ in ${\mathbb R}^n$
to the minimal, average or maximal surface area of its hyperplane
or lower dimensional projections. We discuss the
same questions for all the quermassintegrals of $K$. We examine
separately the dependence of the constants
on the dimension in the case where $K$ is in some of the classical
positions or $K$ is a projection body.
Our results are in the spirit of the hyperplane problem, with
sections replaced by projections and volume by
surface area.
Keywords:surface area, convex body, projection Categories:52A20, 46B05 

24. CJM 2017 (vol 69 pp. 1109)
 Ng, P. W.; Skoufranis, P.

Closed Convex Hulls of Unitary Orbits in Certain Simple Real Rank Zero C$^*$algebras
In this paper, we characterize the closures of convex hulls of
unitary orbits of selfadjoint operators in unital, separable,
simple C$^*$algebras with nontrivial tracial simplex, real
rank zero, stable rank one, and strict comparison of projections
with respect to tracial states. In addition, an upper bound
for the number of unitary conjugates in a convex combination
needed to approximate a selfadjoint are obtained.
Keywords:convex hull of unitary orbits, real rank zero C*algebras simple, eigenvalue function, majorization Category:46L05 

25. CJM 2017 (vol 69 pp. 1064)
 Crann, Jason

Amenability and Covariant Injectivity of Locally Compact Quantum Groups II
Building on our previous work, we study the nonrelative homology
of quantum group convolution algebras. Our main result establishes
the equivalence of amenability of a locally compact quantum group
$\mathbb{G}$ and 1injectivity of
$L^{\infty}(\widehat{\mathbb{G}})$
as an operator
$L^1(\widehat{\mathbb{G}})$module.
In particular, a locally compact group $G$ is amenable if and
only if its group von Neumann algebra
$VN(G)$
is 1injective as
an operator module over the Fourier algebra $A(G)$. As an application,
we provide a decomposability result for completely bounded
$L^1(\widehat{\mathbb{G}})$module
maps on
$L^{\infty}(\widehat{\mathbb{G}})$,
and give a simplified proof that amenable discrete
quantum groups have coamenable compact duals which avoids the
use of modular theory and the PowersStÃ¸rmer inequality, suggesting
that our homological techniques may yield a new approach to the
open problem of duality between amenability and coamenability.
Keywords:locally compact quantum group, amenability, injective module Categories:22D35, 46M10, 46L89 
