1. CJM Online first
2. 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 

3. CJM Online first
 Bickerton, Robert T.; Kakariadis, Evgenios T.A.

Free Multivariate w*Semicrossed Products: Reflexivity and the Bicommutant Property
We study w*semicrossed products over actions of the free semigroup
and the free abelian semigroup on (possibly nonselfadjoint)
w*closed algebras.
We show that they are reflexive when the dynamics are implemented
by uniformly bounded families of invertible row operators.
Combining with results of Helmer we derive that w*semicrossed
products of factors (on a separable Hilbert space) are reflexive.
Furthermore we show that w*semicrossed products of automorphic
actions on maximal abelian selfadjoint algebras are reflexive.
In all cases we prove that the w*semicrossed products have the
bicommutant property if and only if the ambient algebra of the
dynamics does also.
Keywords:reflexivity, semicrossed product Categories:47A15, 47L65, 47L75, 47L80 

4. 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 

5. CJM 2017 (vol 70 pp. 515)
 Chen, Yanni; Hadwin, Don; Liu, Zhe; Nordgren, Eric

A Beurling Theorem for Generalized Hardy Spaces on a Multiply Connected Domain
The object of this paper is to prove a version of the BeurlingHelsonLowdenslager
invariant subspace theorem for operators on certain Banach spaces
of functions on a multiply connected domain in $\mathbb{C}$. The norms
for these spaces are either the usual Lebesgue and Hardy space
norms or certain continuous gauge norms.
In the Hardy space case the expected corollaries include the
characterization of the cyclic vectors as the outer functions
in this context, a demonstration that the set of analytic multiplication
operators is maximal abelian and reflexive, and a determination
of the closed operators that commute with all analytic multiplication
operators.
Keywords:Beurling theorem, invariant subspace, generalized Hardy space, gauge norm, multiply connected domain, Forelli projection, innerouter factorization, affiliated operator Categories:47L10, 30H10 

6. CJM 2017 (vol 70 pp. 97)
 Ghaani Farashahi, Arash

A Class of Abstract Linear Representations for Convolution Function Algebras over Homogeneous Spaces of Compact Groups
This paper introduces a class of abstract linear representations
on
Banach convolution function algebras over
homogeneous spaces of compact groups. Let $G$ be a compact group
and $H$ be a closed subgroup of $G$.
Let $\mu$ be the normalized $G$invariant measure over the compact
homogeneous space $G/H$ associated to the
Weil's formula and $1\le p\lt \infty$.
We then present a structured class of abstract linear representations
of the
Banach convolution function algebras $L^p(G/H,\mu)$.
Keywords:homogeneous space, linear representation, continuous unitary representation, convolution function algebra, compact group, convolution, involution Categories:43A85, 47A67, 20G05 

7. CJM 2016 (vol 69 pp. 1422)
 Šemrl, Peter

Order and Spectrum Preserving Maps on Positive Operators
We describe the general form of surjective maps on the cone of
all positive operators which preserve order and spectrum. The
result is optimal as shown by
counterexamples. As an easy consequence we characterize surjective
order and spectrum preserving maps on the set of all selfadjoint
operators.
Keywords:spectrum preserver, order preserver, positive operator Category:47B49 

8. CJM 2016 (vol 69 pp. 650)
 Oikhberg, Timur; Tradacete, Pedro

Almost Disjointness Preservers
We study the stability of disjointness preservers on Banach lattices.
In many cases, we prove that an "almost disjointness preserving"
operator is well approximable by a disjointness preserving one.
However, this approximation is not always possible, as our
examples show.
Keywords:Banach lattice, disjointness preserving Categories:47B38, 46B42 

9. CJM 2016 (vol 69 pp. 434)
 Lee, Hun Hee; Youn, Sanggyun

New Deformations of Convolution Algebras and Fourier Algebras on Locally Compact Groups
In this paper we introduce a new way of deforming convolution
algebras and Fourier algebras on locally compact groups. We demonstrate
that this new deformation allows us to reveal some information
of the underlying groups by examining Banach algebra properties
of deformed algebras. More precisely, we focus on representability
as an operator algebra of deformed convolution algebras on compact
connected Lie groups with connection to the real dimension of
the underlying group. Similarly, we investigate complete representability
as an operator algebra of deformed Fourier algebras on some finitely
generated discrete groups with connection to the growth rate
of the group.
Keywords:Fourier algebra, convolution algebra, operator algebra, Beurling algebra Categories:43A20, 43A30, 47L30, 47L25 

10. CJM 2016 (vol 69 pp. 373)
 Kaftal, Victor; Ng, Ping Wong; Zhang, Shuang

Strict Comparison of Positive Elements in Multiplier Algebras
Main result: If a C*algebra $\mathcal{A}$ is simple, $\sigma$unital,
has finitely many extremal traces, and has strict comparison
of positive elements by traces, then its multiplier algebra
$\operatorname{\mathcal{M}}(\mathcal{A})$
also has strict comparison of positive elements by traces. The
same results holds if ``finitely many extremal traces" is replaced
by ``quasicontinuous scale".
A key ingredient in the proof is that every positive element
in the multiplier algebra of an arbitrary $\sigma$unital C*algebra
can be approximated by a bidiagonal series.
An application of strict comparison: If $\mathcal{A}$ is a simple separable
stable C*algebra with real rank zero, stable rank one, and
strict comparison of positive elements by traces, then whether
a positive element is a positive linear combination of projections
is determined by the trace values of its range projection.
Keywords:strict comparison, bidiagonal form, positive combinations Categories:46L05, 46L35, 46L45, 47C15 

11. CJM 2016 (vol 69 pp. 54)
 Hartz, Michael

On the Isomorphism Problem for Multiplier Algebras of NevanlinnaPick Spaces
We continue the investigation of the isomorphism problem for
multiplier algebras of reproducing kernel
Hilbert spaces with the complete NevanlinnaPick property.
In contrast to previous work in this area,
we do not study these spaces by identifying them with restrictions
of a universal space, namely the DruryArveson space.
Instead, we work directly with the Hilbert spaces and their
reproducing kernels. In particular,
we show that two multiplier algebras of NevanlinnaPick spaces
on the same set are equal if and only if the Hilbert
spaces are equal. Most of the article is devoted to the study
of a special class of
complete NevanlinnaPick spaces on homogeneous varieties. We
provide a complete
answer to the question of when two multiplier algebras of spaces
of this type
are algebraically or isometrically isomorphic. This generalizes
results of Davidson, Ramsey, Shalit,
and the author.
Keywords:nonselfadjoint operator algebras, reproducing kernel Hilbert spaces, multiplier algebra, NevanlinnaPick kernels, isomorphism problem Categories:47L30, 46E22, 47A13 

12. CJM 2016 (vol 68 pp. 1257)
13. CJM 2016 (vol 68 pp. 816)
 Guo, Xiaoli; Hu, Guoen

On the Commutators of Singular Integral Operators with Rough Convolution Kernels
Let $T_{\Omega}$ be the singular integral operator with kernel
$\frac{\Omega(x)}{x^n}$, where $\Omega$ is homogeneous of degree
zero, has mean value zero and belongs to $L^q(S^{n1})$ for
some
$q\in (1,\,\infty]$. In this paper, the authors establish the
compactness on weighted $L^p$ spaces, and the Morrey spaces,
for the commutator generated by $\operatorname{CMO}(\mathbb{R}^n)$ function
and $T_{\Omega}$. The associated maximal operator and the discrete
maximal operator are also considered.
Keywords:commutator, singular integral operator, compact operator, completely continuous operator, maximal operator, Morrey space Categories:42B20, 47B07 

14. CJM 2016 (vol 68 pp. 309)
 Daws, Matthew

Categorical Aspects of Quantum Groups: Multipliers and Intrinsic Groups
We show that the assignment of the (left) completely bounded
multiplier algebra
$M_{cb}^l(L^1(\mathbb G))$ to a locally compact quantum group
$\mathbb G$, and
the assignment of the intrinsic group, form functors between
appropriate
categories. Morphisms of locally compact quantum
groups can be described by Hopf $*$homomorphisms between universal
$C^*$algebras, by bicharacters, or by special sorts of coactions.
We show that the whole
theory of completely bounded multipliers can be lifted to the
universal
$C^*$algebra level, and that then the different pictures of
both multipliers
(reduced, universal, and as centralisers)
and morphisms interact in extremely natural ways. The intrinsic
group of a
quantum group can be realised as a class of multipliers, and
so our techniques
immediately apply. We also show how to think of the intrinsic
group using
the universal $C^*$algebra picture, and then, again, show how
the differing
views on the intrinsic group interact naturally with morphisms.
We show that
the intrinsic group is the ``maximal classical'' quantum subgroup
of a locally
compact quantum group, show that it is even closed in the strong
Vaes sense,
and that the intrinsic group functor is an adjoint to the inclusion
functor
from locally compact groups to quantum groups.
Keywords:locally compact quantum group, morphism, intrinsic group, multiplier, centraliser Categories:20G42, 22D25, 43A22, 43A35, 43A95, 46L52, 46L89, 47L25 

15. CJM 2015 (vol 69 pp. 408)
 Klep, Igor; Špenko, Špela

Free Function Theory Through Matrix Invariants
This paper concerns free function theory. Free maps are free
analogs of analytic functions in several complex variables,
and are defined in terms of freely noncommuting variables.
A function of $g$ noncommuting variables is a function on $g$tuples
of square matrices of all sizes that respects direct sums and
simultaneous conjugation.
Examples of such maps include noncommutative polynomials, noncommutative
rational functions and convergent noncommutative power series.
In sharp contrast to the existing literature in free analysis, this article
investigates free maps \emph{with involution} 
free analogs of real analytic functions.
To
get a grip on these,
techniques and tools from invariant theory are developed and
applied to free analysis. Here is a sample of the results obtained.
A characterization of polynomial free maps via properties of
their finitedimensional slices is presented and then used to
establish power series expansions for analytic free maps about
scalar and nonscalar points; the latter are series of generalized
polynomials for which an invarianttheoretic characterization
is given.
Furthermore,
an inverse and implicit function theorem for free maps with
involution is obtained.
Finally, with a selection of carefully chosen examples
it is shown that
free maps with involution
do not exhibit strong rigidity properties
enjoyed by their involutionfree
counterparts.
Keywords:free algebra, free analysis, invariant theory, polynomial identities, trace identities, concomitants, analytic maps, inverse function theorem, generalized polynomials Categories:16R30, 32A05, 46L52, 15A24, 47A56, 15A24, 46G20 

16. CJM 2015 (vol 67 pp. 1384)
 Graczyk, Piotr; Kemp, Todd; Loeb, JeanJacques

Strong Logarithmic Sobolev Inequalities for LogSubharmonic Functions
We prove an intrinsic equivalence between strong
hypercontractivity and a strong logarithmic Sobolev
inequality for the cone of logarithmically subharmonic
(LSH) functions. We introduce a new large class of measures,
Euclidean regular and exponential type, in addition to all compactlysupported
measures, for which this equivalence holds. We prove a Sobolev
density theorem through LSH functions and use it to prove
the equivalence of strong
hypercontractivity and the strong logarithmic Sobolev
inequality for such logsubharmonic
functions.
Keywords:logarithmic Sobolev inequalities Category:47D06 

17. CJM 2014 (vol 66 pp. 1110)
 Li, Dong; Xu, Guixiang; Zhang, Xiaoyi

On the Dispersive Estimate for the Dirichlet SchrÃ¶dinger Propagator and Applications to Energy Critical NLS
We consider the obstacle problem for the SchrÃ¶dinger evolution
in the exterior of the unit ball with Dirichlet boundary condition. Under
the radial symmetry we compute explicitly the fundamental solution
for the linear Dirichlet SchrÃ¶dinger
propagator $e^{it\Delta_D}$
and give a robust algorithm to prove sharp $L^1 \rightarrow
L^{\infty}$ dispersive estimates. We showcase the analysis in
dimensions $n=5,7$. As an application, we obtain global
wellposedness and scattering for defocusing energycritical NLS on
$\Omega=\mathbb{R}^n\backslash \overline{B(0,1)}$ with Dirichlet boundary
condition and radial data in these dimensions.
Keywords:Dirichlet SchrÃ¶dinger propagator, dispersive estimate, Dirichlet boundary condition, scattering theory, energy critical Categories:35P25, 35Q55, 47J35 

18. CJM 2013 (vol 67 pp. 132)
 Clouâtre, Raphaël

Unitary Equivalence and Similarity to Jordan Models for Weak Contractions of Class $C_0$
We obtain results on the unitary equivalence of weak contractions of
class $C_0$ to their Jordan models under an assumption on their
commutants. In particular, our work addresses the case of arbitrary
finite multiplicity. The main tool is the
theory of boundary representations due to Arveson. We also
generalize and improve previously known results concerning unitary
equivalence and similarity to Jordan models when the minimal function
is a Blaschke product.
Keywords:weak contractions, operators of class $C_0$, Jordan model, unitary equivalence Categories:47A45, 47L55 

19. CJM 2013 (vol 66 pp. 1143)
 Plevnik, Lucijan; Šemrl, Peter

Maps Preserving Complementarity of Closed Subspaces of a Hilbert Space
Let $\mathcal{H}$ and $\mathcal{K}$ be infinitedimensional separable
Hilbert spaces and ${\rm Lat}\,\mathcal{H}$ the lattice of all closed subspaces oh $\mathcal{H}$.
We describe the general form of pairs of bijective maps $\phi , \psi :
{\rm Lat}\,\mathcal{H} \to {\rm Lat}\,\mathcal{K}$ having the property that for every pair
$U,V \in {\rm Lat}\,\mathcal{H}$ we have $\mathcal{H} = U \oplus V \iff \mathcal{K} = \phi (U) \oplus \psi (V)$. Then we reformulate this theorem as a description
of bijective image equality and kernel equality preserving maps acting on bounded linear idempotent operators. Several known
structural results for maps on idempotents are easy consequences.
Keywords:Hilbert space, lattice of closed subspaces, complemented subspaces, adjacent subspaces, idempotents Categories:46B20, 47B49 

20. CJM 2013 (vol 65 pp. 1005)
 Forrest, Brian; Miao, Tianxuan

Uniformly Continuous Functionals and MWeakly Amenable Groups
Let $G$ be a locally compact group. Let $A_{M}(G)$ ($A_{0}(G)$)denote
the closure of $A(G)$, the Fourier algebra of $G$ in the space of
bounded (completely bounded) multipliers of $A(G)$.
We call a locally compact group Mweakly amenable if
$A_M(G)$
has a
bounded approximate identity. We will show that when $G$ is Mweakly
amenable, the algebras $A_{M}(G)$ and $A_{0}(G)$ have
properties that are characteristic of the Fourier algebra of an
amenable group. Along the way we show that the sets of tolopolically
invariant means associated with these algebras have the same
cardinality as those of the Fourier algebra.
Keywords:Fourier algebra, multipliers, weakly amenable, uniformly continuous functionals Categories:43A07, 43A22, 46J10, 47L25 

21. CJM 2013 (vol 66 pp. 387)
 Mashreghi, J.; Shabankhah, M.

Composition of Inner Functions
We study the image of the model subspace $K_\theta$ under the
composition operator $C_\varphi$, where $\varphi$ and $\theta$ are
inner functions, and find the smallest model subspace which contains
the linear manifold $C_\varphi K_\theta$. Then we characterize the
case when $C_\varphi$ maps $K_\theta$ into itself. This case leads to
the study of the inner functions $\varphi$ and $\psi$ such that the
composition $\psi\circ\varphi$ is a divisor of $\psi$ in the family of
inner functions.
Keywords:composition operators, inner functions, Blaschke products, model subspaces Categories:30D55, 30D05, 47B33 

22. CJM 2013 (vol 65 pp. 783)
 Garcés, Jorge J.; Peralta, Antonio M.

Generalised Triple Homomorphisms and Derivations
We introduce generalised triple homomorphism between Jordan Banach
triple systems as a concept which extends the notion of generalised homomorphism between
Banach algebras given by K. Jarosz and B.E. Johnson in 1985 and 1987, respectively.
We prove that every generalised triple homomorphism between JB$^*$triples
is automatically continuous. When particularised to C$^*$algebras, we rediscover
one of the main theorems established by B.E. Johnson. We shall also consider generalised
triple derivations from a Jordan Banach triple $E$ into a Jordan Banach triple $E$module,
proving that every generalised triple derivation from a JB$^*$triple $E$ into itself or into $E^*$
is automatically continuous.
Keywords:generalised homomorphism, generalised triple homomorphism, generalised triple derivation, Banach algebra, Jordan Banach triple, C$^*$algebra, JB$^*$triple Categories:46L05, 46L70, 47B48, 17C65, 46K70, 46L40, 47B47, 47B49 

23. CJM 2013 (vol 66 pp. 641)
 Grigor'yan, Alexander; Hu, Jiaxin

Heat Kernels and Green Functions on Metric Measure Spaces
We prove that, in a setting of local Dirichlet forms on metric measure
spaces, a twosided subGaussian estimate of the heat kernel is equivalent
to the conjunction of the volume doubling propety, the elliptic Harnack
inequality and a certain estimate of the capacity between concentric balls.
The main technical tool is the equivalence between the capacity estimate and
the estimate of a mean exit time in a ball, that uses twosided estimates of
a Green function in a ball.
Keywords:Dirichlet form, heat kernel, Green function, capacity Categories:35K08, 28A80, 31B05, 35J08, 46E35, 47D07 

24. CJM 2012 (vol 65 pp. 768)
 Fuller, Adam Hanley

Nonselfadjoint Semicrossed Products by Abelian Semigroups
Let $\mathcal{S}$ be the semigroup $\mathcal{S}=\sum^{\oplus k}_{i=1}\mathcal{S}_i$, where for each $i\in I$,
$\mathcal{S}_i$ is a countable subsemigroup of the additive semigroup $\mathbb{R}_+$ containing $0$. We consider representations
of $\mathcal{S}$ as contractions $\{T_s\}_{s\in\mathcal{S}}$ on a Hilbert space with the Nicacovariance property:
$T_s^*T_t=T_tT_s^*$ whenever $t\wedge s=0$. We show that all such representations have a unique minimal isometric Nicacovariant
dilation.
This result is used to help analyse the nonselfadjoint semicrossed product algebras formed from Nicacovariant representations of the action of $\mathcal{S}$ on an operator algebra $\mathcal{A}$ by completely contractive endomorphisms.
We conclude by calculating the $C^*$envelope of the isometric nonselfadjoint semicrossed product algebra (in the sense
of Kakariadis and Katsoulis).
Keywords:semicrossed product, crossed product, C*envelope, dilations Categories:47L55, 47A20, 47L65 

25. CJM 2011 (vol 64 pp. 1329)