51. 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 

52. CJM 2010 (vol 62 pp. 595)
53. CJM 2009 (vol 62 pp. 242)
54. 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 

55. 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 

56. 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 

57. 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 

58. 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 

59. 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 

60. 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 

61. CJM 2009 (vol 61 pp. 50)
62. 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 

63. 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 

64. 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 

65. CJM 2008 (vol 60 pp. 975)
 Boca, Florin P.

An AF Algebra Associated with the Farey Tessellation
We associate with the Farey tessellation of the upper
halfplane an
AF algebra $\AA$ encoding the ``cutting sequences'' that define
vertical geodesics.
The EffrosShen AF algebras arise as quotients
of $\AA$. Using the path algebra model for AF algebras we construct, for
each $\tau \in \big(0,\frac{1}{4}\big]$, projections $(E_n)$ in
$\AA$ such that $E_n E_{n\pm 1}E_n \leq \tau E_n$.
Categories:46L05, 11A55, 11B57, 46L55, 37E05, 82B20 

66. CJM 2008 (vol 60 pp. 520)
 Chen, ChangPao; Huang, HaoWei; Shen, ChunYen

Matrices Whose Norms Are Determined by Their Actions on Decreasing Sequences
Let $A=(a_{j,k})_{j,k \ge 1}$ be a nonnegative matrix. In this
paper, we characterize those $A$ for which $\A\_{E, F}$ are
determined by their actions on decreasing sequences, where $E$ and
$F$ are suitable normed Riesz spaces of sequences. In particular,
our results can apply to the following spaces: $\ell_p$, $d(w,p)$,
and $\ell_p(w)$. The results established here generalize
ones given by Bennett; Chen, Luor, and Ou; Jameson; and
Jameson and Lashkaripour.
Keywords:norms of matrices, normed Riesz spaces, weighted mean matrices, NÃ¶rlund mean matrices, summability matrices, matrices with row decreasing Categories:15A60, 40G05, 47A30, 47B37, 46B42 

67. CJM 2008 (vol 60 pp. 703)
 Toms, Andrew S.; Winter, Wilhelm

$\mathcal{Z}$Stable ASH Algebras
The JiangSu algebra $\mathcal{Z}$ has come to prominence in the
classification program for nuclear $C^*$algebras of late, due
primarily to the fact that Elliott's classification conjecture in its
strongest form predicts that all simple, separable, and nuclear
$C^*$algebras with unperforated $\mathrm{K}$theory will absorb
$\mathcal{Z}$ tensorially, i.e., will be $\mathcal{Z}$stable. There
exist counterexamples which suggest that the conjecture will only hold
for simple, nuclear, separable and $\mathcal{Z}$stable
$C^*$algebras. We prove that virtually all classes of nuclear
$C^*$algebras for which the Elliott conjecture has been confirmed so
far consist of $\mathcal{Z}$stable $C^*$algebras. This
follows in large part from the following result, also proved herein:
separable and approximately divisible $C^*$algebras are
$\mathcal{Z}$stable.
Keywords:nuclear $C^*$algebras, Ktheory, classification Categories:46L85, 46L35 

68. CJM 2008 (vol 60 pp. 189)
 Lin, Huaxin

Furstenberg Transformations and Approximate Conjugacy
Let $\alpha$ and
$\beta$ be two Furstenberg transformations on $2$torus associated
with irrational numbers $\theta_1,$ $\theta_2,$ integers $d_1, d_2$ and Lipschitz functions
$f_1$ and $f_2$. It is shown that $\alpha$ and $\beta$ are approximately conjugate in a
measure theoretical sense if (and only
if) $\overline{\theta_1\pm \theta_2}=0$ in $\R/\Z.$ Closely related to the classification of simple
amenable \CAs, it is shown that $\af$ and $\bt$ are approximately $K$conjugate if (and only if)
$\overline{\theta_1\pm \theta_2}=0$ in $\R/\Z$ and $d_1=d_2.$ This
is also shown to be equivalent to the condition that the associated crossed product \CAs are isomorphic.
Keywords:Furstenberg transformations, approximate conjugacy Categories:37A55, 46L35 

69. CJM 2007 (vol 59 pp. 1135)
 Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari

Sobolev Extensions of HÃ¶lder Continuous and Characteristic Functions on Metric Spaces
We study when characteristic and H\"older continuous functions
are traces of Sobolev functions on doubling metric measure spaces.
We provide analytic and geometric conditions sufficient for extending
characteristic and H\"older continuous functions into globally defined
Sobolev functions.
Keywords:characteristic function, Newtonian function, metric space, resolutivity, HÃ¶lder continuous, Perron solution, $p$harmonic, Sobolev extension, Whitney covering Categories:46E35, 31C45 

70. CJM 2007 (vol 59 pp. 1029)
 Kalton, N. J.; Koldobsky, A.; Yaskin, V.; Yaskina, M.

The Geometry of $L_0$
Suppose that we have the unit Euclidean ball in
$\R^n$ and construct new bodies using three operations  linear
transformations, closure in the radial metric, and multiplicative
summation defined by $\x\_{K+_0L} = \sqrt{\x\_K\x\_L}.$ We prove
that in dimension $3$ this procedure gives all originsymmetric convex
bodies, while this is no longer true in dimensions $4$ and higher. We
introduce the concept of embedding of a normed space in $L_0$ that
naturally extends the corresponding properties of $L_p$spaces with
$p\ne0$, and show that the procedure described above gives exactly the
unit balls of subspaces of $L_0$ in every dimension. We provide
Fourier analytic and geometric characterizations of spaces embedding
in $L_0$, and prove several facts confirming the place of $L_0$ in the
scale of $L_p$spaces.
Categories:52A20, 52A21, 46B20 

71. CJM 2007 (vol 59 pp. 966)
 Forrest, Brian E.; Runde, Volker; Spronk, Nico

Operator Amenability of the Fourier Algebra in the $\cb$Multiplier Norm
Let $G$ be a locally compact group, and let $A_{\cb}(G)$ denote the
closure of $A(G)$, the Fourier algebra of $G$, in the space of completely
bounded multipliers of $A(G)$. If $G$ is a weakly amenable, discrete group
such that $\cstar(G)$ is residually finitedimensional, we show that
$A_{\cb}(G)$ is operator amenable. In particular,
$A_{\cb}(\free_2)$ is operator amenable even though $\free_2$, the free
group in two generators, is not an amenable group. Moreover, we show that
if $G$ is a discrete group such that $A_{\cb}(G)$ is operator amenable,
a closed ideal of $A(G)$ is weakly completely complemented in $A(G)$
if and only if it has an approximate identity bounded in the $\cb$multiplier
norm.
Keywords:$\cb$multiplier norm, Fourier algebra, operator amenability, weak amenability Categories:43A22, 43A30, 46H25, 46J10, 46J40, 46L07, 47L25 

72. CJM 2007 (vol 59 pp. 897)
 Bruneau, Laurent

The Ground State Problem for a Quantum Hamiltonian Model Describing Friction
In this paper, we consider the quantum version of a Hamiltonian model
describing friction.
This model consists of
a particle which interacts with a bosonic reservoir representing a
homogeneous medium through which the particle moves. We show that if
the particle is confined, then the Hamiltonian admits a ground state
if and only if a suitable infrared condition is satisfied. The latter
is violated in the case of linear friction, but satisfied when the
friction force is proportional to a higher power of the particle
speed.
Categories:81Q10, 46N50 

73. CJM 2007 (vol 59 pp. 614)
 Labuschagne, C. C. A.

Preduals and Nuclear Operators Associated with Bounded, $p$Convex, $p$Concave and Positive $p$Summing Operators
We use Krivine's form of the Grothendieck inequality
to renorm the space of bounded linear maps acting between Banach
lattices. We
construct preduals and describe the nuclear operators
associated with these preduals for this renormed space
of bounded operators as well as for
the spaces of $p$convex,
$p$concave and positive $p$summing operators acting
between Banach lattices and Banach spaces.
The nuclear operators obtained are described in
terms of factorizations through
classical Banach spaces via positive operators.
Keywords:$p$convex operator, $p$concave operator, $p$summing operator, Banach space, Banach lattice, nuclear operator, sequence space Categories:46B28, 47B10, 46B42, 46B45 

74. CJM 2007 (vol 59 pp. 276)
 Bernardis, A. L.; MartínReyes, F. J.; Salvador, P. Ortega

Weighted Inequalities for HardySteklov Operators
We characterize the pairs of weights $(v,w)$ for which the
operator $Tf(x)=g(x)\int_{s(x)}^{h(x)}f$ with $s$ and $h$
increasing and continuous functions is of strong type
$(p,q)$ or weak type $(p,q)$ with respect to the pair
$(v,w)$ in the case $0
Keywords:HardySteklov operator, weights, inequalities Categories:26D15, 46E30, 42B25 

75. CJM 2007 (vol 59 pp. 343)
 Lin, Huaxin

Weak Semiprojectivity in Purely Infinite Simple $C^*$Algebras
Let $A$ be a separable amenable purely infinite simple \CA which
satisfies the Universal Coefficient Theorem. We prove that $A$ is
weakly semiprojective if and only if $K_i(A)$ is a countable
direct sum of finitely generated groups ($i=0,1$). Therefore, if
$A$ is such a \CA, for any $\ep>0$ and any finite subset ${\mathcal
F}\subset A$ there exist $\dt>0$ and a finite subset ${\mathcal
G}\subset A$ satisfying the following: for any contractive
positive linear map $L: A\to B$ (for any \CA $B$) with $
\L(ab)L(a)L(b)\<\dt$ for $a, b\in {\mathcal G}$
there exists a homomorphism $h\from A\to B$ such that
$ \h(a)L(a)\<\ep$ for $a\in {\mathcal F}$.
Keywords:weakly semiprojective, purely infinite simple $C^*$algebras Categories:46L05, 46L80 
