51. CJM 2011 (vol 63 pp. 551)
 Hadwin, Don; Li, Qihui; Shen, Junhao

Topological Free Entropy Dimensions in Nuclear C$^*$algebras and in Full Free Products of Unital C$^*$algebras
In the paper, we introduce a new concept,
topological orbit dimension of an $n$tuple of elements in a unital
C$^{\ast}$algebra. Using this concept, we conclude that Voiculescu's
topological free
entropy dimension of every finite family of selfadjoint generators of a
nuclear C$^{\ast}$algebra is less than or equal to $1$. We also show that the
Voiculescu's topological free entropy dimension is additive in the full free
product of some unital C$^{\ast}$algebras. We show that the unital full free
product of Blackadar and Kirchberg's unital MF
algebras is also an MF algebra. As an application, we obtain that
$\mathop{\textrm{Ext}}(C_{r}^{\ast}(F_{2})\ast_{\mathbb{C}}C_{r}^{\ast}(F_{2}))$ is not a group.
Keywords: topological free entropy dimension, unital C$^{*}$algebra Categories:46L10, 46L54 

52. CJM 2011 (vol 63 pp. 460)
 Pavlíček, Libor

Monotonically Controlled Mappings
We study classes of mappings between finite and infinite dimensional
Banach spaces that are monotone and mappings which are differences
of monotone mappings (DM). We prove a RadÃ³Reichelderfer estimate
for monotone mappings in finite dimensional spaces that remains
valid for DM mappings. This provides an alternative proof of the
FrÃ©chet differentiability a.e. of DM mappings. We establish a
Morreytype estimate for the distributional derivative of monotone
mappings. We prove that a locally DM mapping between finite
dimensional spaces is also globally DM. We introduce and study a new
class of the socalled UDM mappings between Banach spaces, which
generalizes the concept of curves of finite variation.
Keywords: monotone mapping, DM mapping, RadÃ³Reichelderfer property, UDM mapping, differentiability Categories:26B05, 46G05 

53. CJM 2011 (vol 63 pp. 381)
 Ji, Kui ; Jiang, Chunlan

A Complete Classification of AI Algebras with the Ideal Property
Let $A$ be an AI algebra; that is, $A$ is the $\mbox{C}^{*}$algebra inductive limit
of a sequence
$$
A_{1}\stackrel{\phi_{1,2}}{\longrightarrow}A_{2}\stackrel{\phi_{2,3}}{\longrightarrow}A_{3}
\longrightarrow\cdots\longrightarrow A_{n}\longrightarrow\cdots,
$$
where
$A_{n}=\bigoplus_{i=1}^{k_n}M_{[n,i]}(C(X^{i}_n))$,
$X^{i}_n$ are $[0,1]$, $k_n$, and
$[n,i]$ are positive integers.
Suppose that $A$ has the
ideal property: each closed twosided ideal of $A$ is generated by
the projections inside the ideal, as a closed twosided ideal.
In this article, we give a complete classification of AI algebras with the ideal property.
Keywords:AI algebras, Kgroup, tracial state, ideal property, classification Categories:46L35, 19K14, 46L05, 46L08 

54. CJM 2011 (vol 63 pp. 500)
 Dadarlat, Marius; Elliott, George A.; Niu, Zhuang

OneParameter Continuous Fields of Kirchberg Algebras. II
Parallel to the first two authors' earlier classification of separable, unita
oneparameter, continuous fields of Kirchberg algebras with torsion free
$\mathrm{K}$groups supported in one dimension, oneparameter, separable, uni
continuous fields of AFalgebras are classified by their ordered
$\mathrm{K}_0$sheaves. EffrosHandelmanShen type theorems are pr separable
unital oneparameter continuous fields of AFalgebras and Kirchberg algebras.
Keywords:continuous fields of C$^*$algebras, $\mathrm{K}_0$presheaves, EffrosHandeen type theorem Category:46L35 

55. CJM 2010 (vol 63 pp. 436)
 Mine, Kotaro; Sakai, Katsuro

Simplicial Complexes and Open Subsets of NonSeparable LFSpaces
Let $F$ be a nonseparable LFspace homeomorphic to
the direct sum $\sum_{n\in\mathbb{N}} \ell_2(\tau_n)$,
where $\aleph_0 < \tau_1 < \tau_2 < \cdots$.
It is proved that
every open subset $U$ of $F$ is homeomorphic to the product $K \times F$
for some locally finitedimensional simplicial complex $K$ such that
every vertex $v \in K^{(0)}$ has the star $\operatorname{St}(v,K)$
with $\operatorname{card} \operatorname{St}(v,K)^{(0)} < \tau = \sup\tau_n$
(and $\operatorname{card} K^{(0)} \le \tau$),
and, conversely, if $K$ is such a simplicial complex,
then the product $K \times F$ can be embedded in $F$ as an open set,
where $K$ is the polyhedron of $K$ with the metric topology.
Keywords:LFspace, open set, simplicial complex, metric topology, locally finitedimensional, star, small box product, ANR, $\ell_2(\tau)$, $\ell_2(\tau)$manifold, open embedding, $\sum_{i\in\mathbb{N}}\ell_2(\tau_i)$ Categories:57N20, 46A13, 46T05, 57N17, 57Q05, 57Q40 

56. CJM 2010 (vol 63 pp. 123)
 Granirer, Edmond E.

Strong and Extremely Strong Ditkin sets for the Banach Algebras $A_p^r(G)=A_p\cap L^r(G)$
Let $A_p(G)$ be the FigaTalamanca,
Herz Banach Algebra on $G$; thus $A_2(G)$
is the Fourier algebra. Strong Ditkin (SD) and
Extremely Strong Ditkin (ESD) sets for the Banach algebras
$A_p^r(G)$ are investigated for abelian and nonabelian
locally compact groups $G$. It is shown that SD and ESD sets
for $A_p(G)$ remain SD and ESD sets for $A_p^r(G)$,
with strict inclusion for ESD sets. The case for the strict
inclusion of SD sets is left open.
A result on the weak sequential completeness of $A_2(F)$
for ESD sets $F$ is proved and used to show that Varopoulos,
Helson, and Sidon sets are not ESD sets for $A_2(G)$, yet they
are such for $A_2^r(G)$ for discrete groups $G$, for
any $1\le r\le 2$.
A result is given on the equivalence of the sequential and the net
definitions of SD or ESD sets for $\sigma$compact groups.
The above results are new even if $G$ is abelian.
Keywords:Fourier algebra, FigaTalamancaHerz algebra, locally compact group, Ditkin sets, Helson sets, Sidon sets, weak sequential completeness Categories:43A15, 43A10, 46J10, 43A45 

57. CJM 2010 (vol 63 pp. 222)
 Wang, JiunChau

Limit Theorems for Additive Conditionally Free Convolution
In this paper we determine the limiting distributional behavior for
sums of infinitesimal conditionally free random variables. We show that the weak
convergence of classical convolution and that of conditionally free convolution
are equivalent for measures in an infinitesimal triangular array,
where the measures may have unbounded support. Moreover, we use these
limit theorems to study the conditionally free infinite divisibility. These results
are obtained by complex analytic methods without reference to the
combinatorics of cfree convolution.
Keywords:additive cfree convolution, limit theorems, infinitesimal arrays Categories:46L53, 60F05 

58. CJM 2010 (vol 63 pp. 3)
 Banica, T.; Belinschi, S. T.; Capitaine, M.; Collins, B.

Free Bessel Laws
We introduce and study a remarkable family of real probability
measures $\pi_{st}$ that we call free Bessel laws. These are related
to the free Poisson law $\pi$ via the formulae
$\pi_{s1}=\pi^{\boxtimes s}$ and ${\pi_{1t}=\pi^{\boxplus t}}$. Our
study includes definition and basic properties, analytic aspects
(supports, atoms, densities), combinatorial aspects (functional
transforms, moments, partitions), and a discussion of the relation
with random matrices and quantum groups.
Keywords:Poisson law, Bessel function, Wishart matrix, quantum group Categories:46L54, 15A52, 16W30 

59. CJM 2010 (vol 62 pp. 961)
 Aleman, Alexandru; Duren, Peter; Martín, María J.; Vukotić, Dragan

Multiplicative Isometries and Isometric ZeroDivisors
For some Banach spaces of analytic functions in the unit disk
(weighted Bergman spaces, Bloch space, Dirichlettype spaces), the
isometric pointwise multipliers are found to be unimodular constants.
As a consequence, it is shown that none of those spaces have isometric
zerodivisors. Isometric coefficient multipliers are also
investigated.
Keywords:Banach spaces of analytic functions, Hardy spaces, Bergman spaces, Bloch space, Dirichlet space, Dirichlettype spaces, pointwise multipliers, coefficient multipliers, isometries, isometric zerodivisors Categories:30H05, 46E15 

60. CJM 2010 (vol 62 pp. 845)
 Samei, Ebrahim; Spronk, Nico; Stokke, Ross

Biflatness and PseudoAmenability of Segal Algebras
We investigate generalized amenability and biflatness properties of various (operator) Segal algebras in both the group algebra, $L^1(G)$, and the Fourier algebra, $A(G)$, of a locally compact group~$G$.
Keywords:Segal algebra, pseudoamenable Banach algebra, biflat Banach algebra Categories:43A20, 43A30, 46H25, 46H10, 46H20, 46L07 

61. CJM 2010 (vol 62 pp. 827)
 Ouyang, Caiheng; Xu, Quanhua

BMO Functions and Carleson Measures with Values in Uniformly Convex Spaces
This paper studies the relationship between vectorvalued BMO functions and the Carleson measures defined by their gradients. Let $dA$ and $dm$ denote Lebesgue measures on the unit disc $D$ and the unit circle $\mathbf{T}$, respectively. For $1< q<\infty$ and a Banach space $B$, we prove that there exists a positive constant $c$ such that $$\sup_{z_0\in D}\int_{D}(1z)^{q1}\\nabla f(z)\^q P_{z_0}(z) dA(z) \le c^q\sup_{z_0\in D}\int_{\mathbf{T}}\f(z)f(z_0)\^qP_{z_0}(z) dm(z)$$ holds for all trigonometric polynomials $f$ with coefficients in $B$ if and only if $B$ admits an equivalent norm which is $q$uniformly convex, where $$P_{z_0}(z)=\frac{1z_0^2}{1\bar{z_0}z^2} .$$ The validity of the converse inequality is equivalent to the existence of an equivalent $q$uniformly smooth norm.
Keywords:BMO, Carleson measures, Lusin type, Lusin cotype, uniformly convex spaces, uniformly smooth spaces Categories:46E40, 42B25, 46B20 

62. CJM 2010 (vol 62 pp. 889)
 Xia, Jingbo

Singular Integral Operators and Essential Commutativity on the Sphere
Let ${\mathcal T}$ be the $C^\ast $algebra generated by the Toeplitz operators $\{T_\varphi : \varphi \in L^\infty (S,d\sigma )\}$ on the Hardy space $H^2(S)$ of the unit sphere in $\mathbf{C}^n$. It is well known that ${\mathcal T}$ is contained in the essential commutant of $\{T_\varphi : \varphi \in \operatorname{VMO}\cap L^\infty (S,d\sigma )\}$. We show that the essential commutant of $\{T_\varphi : \varphi \in \operatorname{VMO}\cap L^\infty (S,d\sigma )\}$ is strictly larger than ${\mathcal T}$.
Categories:32A55, 46L05, 47L80 

63. CJM 2010 (vol 62 pp. 595)
64. CJM 2009 (vol 62 pp. 305)
 Hua, He; Yunbai, Dong; Xianzhou, Guo

Approximation and Similarity Classification of Stably Finitely Strongly Irreducible Decomposable Operators
Let $\mathcal H$ be a complex separable Hilbert space and ${\mathcal L}({\mathcal H})$ denote the collection of bounded linear operators on ${\mathcal H}$. In this paper, we show that for any operator $A\in{\mathcal L}({\mathcal H})$, there exists a stably finitely (SI) decomposable operator $A_\epsilon$, such that $\AA_{\epsilon}\<\epsilon$ and ${\mathcal{\mathcal A}'(A_{\epsilon})}/\operatorname{rad} {{\mathcal A}'(A_{\epsilon})}$ is commutative, where $\operatorname{rad}{{\mathcal A}'(A_{\epsilon})}$ is the Jacobson radical of ${{\mathcal A}'(A_{\epsilon})}$. Moreover, we give a similarity classification of the stably finitely decomposable operators that generalizes the result on similarity classification of CowenDouglas operators given by C. L. Jiang.
Keywords:$K_{0}$group, strongly irreducible decomposition, CowenâDouglas operators, commutant algebra, similarity classification Categories:47A05, 47A55, 46H20 

65. CJM 2009 (vol 62 pp. 646)
 Rupp, R.; Sasane, A.

Reducibility in A_{R}(K), C_{R}(K), and A(K)
Let $K$ denote a compact real symmetric subset of $\mathbb{C}$ and let
$A_{\mathbb R}(K)$ denote the real Banach algebra of all real
symmetric continuous functions on $K$ that are analytic in the
interior $K^\circ$ of $K$, endowed with the supremum norm. We
characterize all unimodular pairs $(f,g)$ in $A_{\mathbb R}(K)^2$
which are reducible.
In addition, for an arbitrary compact $K$ in $\mathbb C$, we give a
new proof (not relying on Banach algebra theory or elementary stable
rank techniques) of the fact that the Bass stable rank of $A(K)$ is
$1$.
Finally, we also characterize all compact real symmetric sets $K$ such
that $A_{\mathbb R}(K)$, respectively $C_{\mathbb R}(K)$, has Bass
stable rank $1$.
Keywords:real Banach algebras, Bass stable rank, topological stable rank, reducibility Categories:46J15, 19B10, 30H05, 93D15 

66. CJM 2009 (vol 62 pp. 242)
67. CJM 2009 (vol 61 pp. 1239)
 Davidson, Kenneth R.; Yang, Dilian

Periodicity in Rank 2 Graph Algebras
Kumjian and Pask introduced an aperiodicity condition
for higher rank graphs.
We present a detailed analysis of when this occurs
in certain rank 2 graphs.
When the algebra is aperiodic, we give another proof
of the simplicity of $\mathrm{C}^*(\mathbb{F}^+_{\theta})$.
The periodic $\mathrm{C}^*$algebras are characterized, and it is shown
that $\mathrm{C}^*(\mathbb{F}^+_{\theta}) \simeq
\mathrm{C}(\mathbb{T})\otimes\mathfrak{A}$
where $\mathfrak{A}$ is a simple $\mathrm{C}^*$algebra.
Keywords:higher rank graph, aperiodicity condition, simple $\mathrm{C}^*$algebra, expectation Categories:47L55, 47L30, 47L75, 46L05 

68. CJM 2009 (vol 61 pp. 1262)
 Dong, Z.

On the Local Lifting Properties of Operator Spaces
In this paper, we mainly study operator spaces which have the
locally lifting property (LLP). The dual of any ternary ring of operators is shown to
satisfy the strongly local reflexivity, and this is used to prove
that strongly local reflexivity holds also for operator spaces
which have the LLP. Several homological characterizations of the
LLP and weak expectation property are given. We also prove that for any operator space
$V$, $V^{**}$ has the LLP if and only if $V$ has the LLP and
$V^{*}$ is exact.
Keywords:operator space, locally lifting property, strongly locally reflexive Category:46L07 

69. CJM 2009 (vol 61 pp. 503)
 Baranov, Anton; Woracek, Harald

Subspaces of de~Branges Spaces Generated by Majorants
For a given de~Branges space $\mc H(E)$ we investigate
de~Branges subspaces defined in terms of majorants
on the real axis. If $\omega$ is a nonnegative function on $\mathbb R$,
we consider the subspace
\[
\mc R_\omega(E)=\clos_{\mc H(E)} \big\{F\in\mc H(E):
\text{ there exists } C>0:
E^{1} F\leq C\omega \mbox{ on }{\mathbb R}\big\}
.
\]
We show that $\mc R_\omega(E)$ is a de~Branges subspace and
describe all subspaces of this form. Moreover,
we give a criterion for the existence of positive minimal majorants.
Keywords:de~Branges subspace, majorant, BeurlingMalliavin Theorem Categories:46E20, 30D15, 46E22 

70. CJM 2009 (vol 61 pp. 282)
 Bouya, Brahim

Closed Ideals in Some Algebras of Analytic Functions
We obtain a complete description of closed ideals of the algebra
$\cD\cap \cL$, $0<\alpha\leq\frac{1}{2}$, where $\cD$ is the
Dirichlet space and $\cL$ is the algebra of analytic functions
satisfying the Lipschitz condition of order $\alpha$.
Categories:46E20, 30H05, 47A15 

71. CJM 2009 (vol 61 pp. 241)
 Azamov, N. A.; Carey, A. L.; Dodds, P. G.; Sukochev, F. A.

Operator Integrals, Spectral Shift, and Spectral Flow
We present a new and simple approach to the theory of multiple
operator integrals that applies to unbounded operators affiliated with general \vNa s.
For semifinite \vNa s we give applications
to the Fr\'echet differentiation of operator functions that sharpen existing results,
and establish the BirmanSolomyak representation of the spectral
shift function of M.\,G.\,Krein
in terms of an average of spectral measures in the type II setting.
We also exhibit a surprising connection between the spectral shift
function and spectral flow.
Categories:47A56, 47B49, 47A55, 46L51 

72. CJM 2009 (vol 61 pp. 124)
 Dijkstra, Jan J.; Mill, Jan van

Characterizing Complete Erd\H os Space
The space now known as {\em complete Erd\H os
space\/} $\cerdos$ was introduced by Paul Erd\H os in 1940 as the
closed subspace of the Hilbert space $\ell^2$ consisting of all
vectors such that every coordinate is in the convergent sequence
$\{0\}\cup\{1/n:n\in\N\}$. In a solution to a problem posed by Lex G.
Oversteegen we present simple and useful topological
characterizations of $\cerdos$.
As an application we determine the class
of factors of $\cerdos$. In another application we determine
precisely which of the spaces that can be constructed in the Banach
spaces $\ell^p$ according to the `Erd\H os method' are homeomorphic
to $\cerdos$. A novel application states that if $I$ is a
Polishable $F_\sigma$ideal on $\omega$, then $I$ with the Polish
topology is homeomorphic to either $\Z$, the Cantor set $2^\omega$,
$\Z\times2^\omega$, or $\cerdos$. This last result answers a
question that was asked
by Stevo Todor{\v{c}}evi{\'c}.
Keywords:Complete Erd\H os space, Lelek fan, almost zerodimensional, nowhere zerodimensional, Polishable ideals, submeasures on $\omega$, $\R$trees, linefree groups in Banach spaces Categories:28C10, 46B20, 54F65 

73. CJM 2009 (vol 61 pp. 50)
74. CJM 2008 (vol 60 pp. 1010)
 Galé, José E.; Miana, Pedro J.

$H^\infty$ Functional Calculus and MikhlinType Multiplier Conditions
Let $T$ be a sectorial operator. It is known that the existence of a
bounded (suitably scaled) $H^\infty$ calculus for $T$, on every
sector containing the positive halfline, is equivalent to the
existence of a bounded functional calculus on the Besov algebra
$\Lambda_{\infty,1}^\alpha(\R^+)$. Such an algebra
includes functions defined by Mikhlintype conditions and so the
Besov calculus can be seen as a result on multipliers for $T$. In
this paper, we use fractional derivation to analyse in detail the
relationship between $\Lambda_{\infty,1}^\alpha$ and Banach algebras
of Mikhlintype. As a result, we obtain a new version of the quoted
equivalence.
Keywords:functional calculus, fractional calculus, Mikhlin multipliers, analytic semigroups, unbounded operators, quasimultipliers Categories:47A60, 47D03, 46J15, 26A33, 47L60, 47B48, 43A22 

75. CJM 2008 (vol 60 pp. 1108)
 LopezAbad, J.; Manoussakis, A.

A Classification of Tsirelson Type Spaces
We give a complete classification of mixed Tsirelson spaces
$T[(\mathcal F_i,\theta_i)_{i=1}^{r}]$ for finitely many pairs of
given compact and hereditary families $\mathcal F_i$ of finite sets of
integers and $0<\theta_i<1$ in terms of the CantorBendixson indices
of the families $\mathcal F_i$, and $\theta_i$ ($1\le i\le r$). We
prove that there are unique countable ordinal $\alpha$ and
$0<\theta<1$ such that every block sequence of
$T[(\mathcal F_i,\theta_i)_{i=1}^{r}]$ has a subsequence equivalent to a
subsequence of the natural basis of the
$T(\mathcal S_{\omega^\alpha},\theta)$. Finally, we give a complete criterion of
comparison in between two of these mixed Tsirelson spaces.
Categories:46B20, 05D10 
