Expand all Collapse all  Results 126  150 of 192 
126. CMB 2005 (vol 48 pp. 97)
On the Ranges of Bimodule Projections We develop a symbol calculus for normal bimodule maps over a masa
that is the natural analogue of the Schur product theory. Using
this calculus we are easily able to give a complete description of
the ranges of contractive normal bimodule idempotents that avoids
the theory of J*algebras.
We prove that if $P$ is a normal
bimodule idempotent and $\P\ < 2/\sqrt{3}$ then $P$ is a
contraction. We finish with some attempts at extending the symbol
calculus to nonnormal maps.
Categories:46L15, 47L25 
127. CMB 2005 (vol 48 pp. 50)
Injectivity of the Connecting Maps in AH Inductive Limit Systems Let $A$ be the inductive limit of a system
$$A_{1}\xrightarrow{\phi_{1,2}}A_{2}
\xrightarrow{\phi_{2,3}} A_{3}\longrightarrow \cd
$$
with $A_n =
\bigoplus_{i=1}^{t_n} P_{n,i}M_{[n,i]}(C(X_{n,i}))P_{n,i}$, where
$~X_{n,i}$ is a finite simplicial complex, and $P_{n,i}$ is a
projection in $M_{[n,i]}(C(X_{n,i}))$. In this paper, we will
prove that $A$ can be written as another inductive limit
$$B_1\xrightarrow{\psi_{1,2}} B_2
\xrightarrow{\psi_{2,3}} B_3\longrightarrow \cd $$
with $B_n =
\bigoplus_{i=1}^{s_n} Q_{n,i}M_{\{n,i\}}(C(Y_{n,i}))Q_{n,i}$,
where $Y_{n,i}$ is a finite simplicial complex, and $Q_{n,i}$ is a
projection in $M_{\{n,i\}}(C(Y_{n,i}))$, with the extra condition
that all the maps $\psi_{n,n+1}$ are \emph{injective}. (The
result is trivial if one allows the spaces $Y_{n,i}$ to be
arbitrary compact metrizable spaces.) This result is important
for the classification of simple AH algebras (see
\cite{G5,G6,EGL}. The special case that the spaces $X_{n,i}$ are
graphs is due to the third named author \cite{Li1}.
Categories:46L05, 46L35, 19K14 
128. CMB 2004 (vol 47 pp. 540)
Compactness of HardyType Operators over StarShaped Regions in $\mathbb{R}^N$ We study a compactness property of the operators between weighted
Lebesgue spaces that average a function over certain domains involving
a starshaped region. The cases covered are (i) when the average is
taken over a difference of two dilations of a starshaped region in
$\RR^N$, and (ii) when the average is taken over all dilations of
starshaped regions in $\RR^N$. These cases include, respectively,
the average over annuli and the average over balls centered at origin.
Keywords:Hardy operator, HardySteklov operator, compactness, boundedness, starshaped regions Categories:46E35, 26D10 
129. CMB 2004 (vol 47 pp. 615)
$C^*$Algebras and Factorization Through Diagonal Operators Let $\cal A$ be a $C^*$algebra and $E$ be a Banach space with
the RadonNikodym property. We prove that if $j$ is an embedding
of $E$ into an injective Banach space then for every absolutely
summing operator $T:\mathcal{A}\longrightarrow E$, the composition
$j \circ T$ factors through a diagonal operator from $l^{2}$ into
$l^{1}$. In particular, $T$ factors through a Banach space with
the Schur property. Similarly, we prove that for $2

130. CMB 2004 (vol 47 pp. 553)
A Geometric Approach to VoiculescuBrown Entropy A basic problem in dynamics is to identify systems
with positive entropy, i.e., systems which are ``chaotic.'' While
there is a vast collection of results addressing this issue in
topological dynamics, the phenomenon of positive entropy remains by and
large a mystery within the broader noncommutative domain of $C^*$algebraic
dynamics. To shed some light on the noncommutative situation we propose
a geometric perspective inspired by work of Glasner and Weiss on
topological entropy.
This is a written version of the author's talk
at the Winter 2002 Meeting of the Canadian Mathematical Society
in Ottawa, Ontario.
Categories:46L55, 37B40 
131. CMB 2004 (vol 47 pp. 481)
A New Characterization of Hardy Martingale Cotype Space We give a new characterization of Hardy martingale cotype
property of complex quasiBanach space by using the existence of a
kind of plurisubharmonic functions. We also characterize the best
constants of Hardy martingale inequalities with values
in the complex quasiBanach space.
Keywords:Hardy martingale, Hardy martingale cotype,, plurisubharmonic function Categories:46B20, 52A07, 60G44 
132. CMB 2004 (vol 47 pp. 445)
Biprojectivity and Biflatness for Convolution Algebras of Nuclear Operators For a locally compact group $G$, the convolution product on
the space $\nN(L^p(G))$ of nuclear operators was defined by Neufang
\cite{Neuf_PhD}. We study homological properties of the convolution algebra
$\nN(L^p(G))$ and relate them to some properties of the group $G$,
such as compactness, finiteness, discreteness, and amenability.
Categories:46M10, 46H25, 43A20, 16E65 
133. CMB 2004 (vol 47 pp. 206)
The PoincarÃ© Inequality and Reverse Doubling Weights We show that Poincar\'e inequalities with reverse doubling weights hold in a
large class of irregular domains whenever the weights satisfy certain
conditions. Examples of these domains are John domains.
Keywords:reverse doubling weights, PoincarÃ© inequality, John domains Category:46E35 
134. CMB 2004 (vol 47 pp. 108)
On Universal Schauder Bases in NonArchimedean FrÃ©chet Spaces It is known that any nonarchimedean Fr\'echet space of countable
type is isomorphic to a subspace of $c_0^{\mathbb{N}}$. In this
paper we prove that there exists a nonarchimedean Fr\'echet space
$U$ with a basis $(u_n)$ such that any basis $(x_n)$ in a
nonarchimedean Fr\'echet space $X$ is equivalent to a subbasis
$(u_{k_n})$ of $(u_n)$. Then any nonarchimedean Fr\'echet space
with a basis is isomorphic to a complemented subspace of $U$. In
contrast to this, we show that a nonarchimedean Fr\'echet space
$X$ with a basis $(x_n)$ is isomorphic to a complemented subspace
of $c_0^{\mathbb{N}}$ if and only if $X$ is isomorphic to one of
the following spaces: $c_0$, $c_0 \times \mathbb{K}^{\mathbb{N}}$,
$\mathbb{K}^{\mathbb{N}}$, $c_0^{\mathbb{N}}$. Finally, we prove
that there is no nuclear nonarchimedean Fr\'echet space $H$ with
a basis $(h_n)$ such that any basis $(y_n)$ in a nuclear
nonarchimedean Fr\'echet space $Y$ is equivalent to a subbasis
$(h_{k_n})$ of $(h_n)$.
Keywords:universal bases, complemented subspaces with bases Categories:46S10, 46A35 
135. CMB 2004 (vol 47 pp. 49)
The Essential Norm of a Blochto$Q_p$ Composition Operator The $Q_p$ spaces coincide with the Bloch space for $p>1$ and are
subspaces of $\BMOA$ for $0

136. CMB 2003 (vol 46 pp. 509)
Symmetries of Kirchberg Algebras Let $G_0$ and $G_1$ be countable abelian groups. Let $\gamma_i$ be an
automorphism of $G_i$ of order two. Then there exists a unital
Kirchberg algebra $A$ satisfying the Universal Coefficient Theorem and
with $[1_A] = 0$ in $K_0 (A)$, and an automorphism $\alpha \in
\Aut(A)$ of order two, such that $K_0 (A) \cong G_0$, such that $K_1
(A) \cong G_1$, and such that $\alpha_* \colon K_i (A) \to K_i (A)$ is
$\gamma_i$. As a consequence, we prove that every
$\mathbb{Z}_2$graded countable module over the representation ring $R
(\mathbb{Z}_2)$ of $\mathbb{Z}_2$ is isomorphic to the equivariant
$K$theory $K^{\mathbb{Z}_2} (A)$ for some action of $\mathbb{Z}_2$ on
a unital Kirchberg algebra~$A$.
Along the way, we prove that every not necessarily finitely generated
$\mathbb{Z} [\mathbb{Z}_2]$module which is free as a
$\mathbb{Z}$module has a direct sum decomposition with only three
kinds of summands, namely $\mathbb{Z} [\mathbb{Z}_2]$ itself and
$\mathbb{Z}$ on which the nontrivial element of $\mathbb{Z}_2$ acts
either trivially or by multiplication by $1$.
Categories:20C10, 46L55, 19K99, 19L47, 46L40, 46L80 
137. CMB 2003 (vol 46 pp. 632)
The Operator Amenability of Uniform Algebras We prove a quantized version of a theorem by M.~V.~She\u{\i}nberg:
A uniform algebra equipped with its canonical, {\it i.e.}, minimal,
operator space structure is operator amenable if and only if it is
a commutative $C^\ast$algebra.
Keywords:uniform algebras, amenable Banach algebras, operator amenability, minimal, operator space Categories:46H20, 46H25, 46J10, 46J40, 47L25 
138. CMB 2003 (vol 46 pp. 588)
Weakly Stable Relations and Inductive Limits of $C^\ast$algebras We show that if $\mathcal{A}$ is a class of $C^\ast$algebras for which
the set of formal relations $\mathcal{R}$ is weakly stable, then $\mathcal{R}$
is weakly stable for the class $\mathcal{B}$ that contains $\mathcal{A}$ and
all the inductive limits that can be constructed with the $C^\ast$algebras in
$\mathcal{A}$.
A set of formal relations $\mathcal{R}$ is said to be {\it weakly stable\/} for
a class $\mathcal{C}$ of $C^\ast$algebras if, in any $C^\ast$algebra $A\in
\mathcal{C}$, close to an approximate representation of the set $\mathcal{R}$
in $A$ there is an exact representation of $\mathcal{R}$ in $A$.
Category:46L05 
139. CMB 2003 (vol 46 pp. 575)
Optimization of Polynomial Functions This paper develops a refinement of Lasserre's algorithm for
optimizing a polynomial on a basic closed semialgebraic set via
semidefinite programming and addresses an open question concerning the
duality gap. It is shown that, under certain natural stability
assumptions, the problem of optimization on a basic closed set reduces
to the compact case.
Categories:14P10, 46L05, 90C22 
140. CMB 2003 (vol 46 pp. 538)
Subdifferentials Whose Graphs Are Not Norm$\times$Weak* Closed In this note we give examples of convex functions whose
subdifferentials have unpleasant properties. Particularly, we
exhibit a proper lower semicontinuous convex function on a
separable Hilbert space such that the graph of its subdifferential
is not closed in the product of the norm and bounded weak
topologies. We also exhibit a set whose sequential normal cone is
not norm closed.
Categories:46N10, 47H05 
141. CMB 2003 (vol 46 pp. 481)
On the Composition of Differentiable Functions We prove that a Banach space $X$ has the Schur property if and only if every
$X$valued weakly differentiable function is Fr\'echet differentiable. We
give a general result on the Fr\'echet differentiability of $f\circ T$, where
$f$ is a Lipschitz function and $T$ is a compact linear operator. Finally
we study, using in particular a smooth variational principle, the
differentiability of the semi norm $\Vert \ \Vert_{\lip}$ on various spaces
of Lipschitz functions.
Categories:58C20, 46B20 
142. CMB 2003 (vol 46 pp. 419)
On NonStrongly Free Automorphisms of Subfactors of Type III$_0$ We determine when an automorphism of a subfactor of type III$_0$
with finite index is nonstrongly free in the sense of C.~Winsl\o w
in terms of the modular endomorphisms introduced by M.~Izumi.
Category:46L37 
143. CMB 2003 (vol 46 pp. 457)
Strongly Perforated $K_{0}$Groups of Simple $C^{*}$Algebras In the sequel we construct simple, unital, separable, stable, amenable
$C^{*}$algebras for which the ordered $K_{0}$group is strongly
perforated and group isomorphic to $Z$. The particular order structures
to be constructed will be described in detail below, and all
known results of this type will be generalised.
Categories:46, 19 
144. CMB 2003 (vol 46 pp. 441)
An Inductive Limit Model for the $K$Theory of the GeneratorInterchanging Antiautomorphism of an Irrational Rotation Algebra 
An Inductive Limit Model for the $K$Theory of the GeneratorInterchanging Antiautomorphism of an Irrational Rotation Algebra Let $A_\theta$ be the universal $C^*$algebra generated by two
unitaries $U$, $V$ satisfying $VU=e^{2\pi i\theta} UV$ and let $\Phi$
be the antiautomorphism of $A_\theta$ interchanging $U$ and $V$. The
$K$theory of $R_\theta=\{a\in A_\theta:\Phi(a)=a^*\}$ is computed. When
$\theta$ is irrational, an inductive limit of algebras of the form
$M_q(C(\mathbb{T})) \oplus M_{q'} (\mathbb{R}) \oplus M_q(\mathbb{R})$
is constructed which has complexification $A_\theta$ and the same
$K$theory as $R_\theta$.
Categories:46L35, 46L80 
145. CMB 2003 (vol 46 pp. 388)
Tracially Quasidiagonal Extensions It is known that a unital simple $C^*$algebra $A$ with tracial
topological rank zero has real rank zero. We show in this note that,
in general, there are unital $C^*$algebras with tracial topological
rank zero that have real rank other than zero.
Let $0\to J\to E\to A\to 0$ be a short exact sequence of
$C^*$algebras. Suppose that $J$ and $A$ have tracial topological
rank zero. It is known that $E$ has tracial topological rank zero
as a $C^*$algebra if and only if $E$ is tracially quasidiagonal
as an extension. We present an example of a tracially
quasidiagonal extension which is not quasidiagonal.
Keywords:tracially quasidiagonal extensions, tracial rank Categories:46L05, 46L80 
146. CMB 2003 (vol 46 pp. 365)
Homogeneity of the Pure State Space of a Separable $C^*$Algebra We prove that the pure state space is homogeneous under the action of
the automorphism group (or the subgroup of asymptotically inner
automorphisms) for all the separable simple $C^*$algebras. The
first result of this kind was shown by Powers for the UHF algbras
some 30 years ago.
Categories:46L40, 46L30 
147. CMB 2003 (vol 46 pp. 242)
Euclidean Sections of Direct Sums of Normed Spaces We study the dimension of ``random'' Euclidean sections of direct sums of
normed spaces. We compare the obtained results with results from \cite{LMS},
to show that for the direct sums the standard randomness with respect to the
Haar measure on Grassmanian coincides with a much ``weaker'' randomness of
``diagonal'' subspaces (Corollary~\ref{sle} and explanation after). We also
add some relative information on ``phase transition''.
Keywords:Dvoretzky theorem, ``random'' Euclidean section, phase transition in asymptotic convexity Categories:46B07, 46B09, 46B20, 52A21 
148. CMB 2003 (vol 46 pp. 164)
Classification of $\AF$ Flows An $\AF$ flow is a oneparameter automorphism group of an $\AF$
$C^*$algebra $A$ such that there exists an increasing sequence of
invariant finite dimensional sub$C^*$algebras whose union is dense in
$A$. In this paper, a classification of $C^*$dynamical systems of
this form up to equivariant isomorphism is presented. Two pictures
of the actions are given, one in terms of a modified Bratteli
diagram/pathspace construction, and one in terms of a modified
$K_0$ functor.
Categories:46L57, 46L35 
149. CMB 2003 (vol 46 pp. 161)
Answer to a Question of S.~Rolewicz We exhibit examples of $F$spaces with trivial dual which are
isomorphic to its quotient by a line, thus solving a problem in
Rolewicz's {\it Metric Linear Spaces}.
Categories:46M99, 46M15, 46A16, 46B20 
150. CMB 2003 (vol 46 pp. 98)
Crossed Products by Semigroups of Endomorphisms and Groups of Partial Automorphisms We consider a class $(A, S, \alpha)$ of dynamical systems,
where $S$ is an Ore semigroup and $\alpha$ is an action such that
each $\alpha_s$ is injective and extendible ({\it i.e.} it extends to a
nonunital endomorphism of the multiplier algebra), and has range an
ideal of $A$. We show that there is a partial action on the fixedpoint
algebra under the canonical coaction of the enveloping group $G$ of $S$
constructed in \cite[Proposition~6.1]{LR2}. It turns out that the full
crossed product by this coaction is isomorphic to $A\rtimes_\alpha S$.
If the coaction is moreover normal, then the isomorphism can be extended
to include the reduced crossed product. We look then at invariant ideals
and finally, at examples of systems where our results apply.
Category:46L55 