Expand all Collapse all  Results 101  125 of 178 
101. CMB 2006 (vol 49 pp. 185)
On the Inequality for Volume and Minkowskian Thickness Given a centrally symmetric convex body $B$ in $\E^d,$ we denote
by $\M^d(B)$ the Minkowski space ({\em i.e.,} finite dimensional
Banach space) with unit ball $B.$ Let $K$ be an arbitrary convex
body in $\M^d(B).$ The relationship between volume $V(K)$ and the
Minkowskian thickness ($=$ minimal width) $\thns_B(K)$ of $K$ can
naturally be given by the sharp geometric inequality $V(K) \ge
\alpha(B) \cdot \thns_B(K)^d,$ where $\alpha(B)>0.$ As a simple
corollary of the RogersShephard inequality we obtain that
$\binom{2d}{d}{}^{1} \le \alpha(B)/V(B) \le 2^{d}$ with equality
on the left attained if and only if $B$ is the difference body of
a simplex and on the right if $B$ is a crosspolytope. The main
result of this paper is that for $d=2$ the equality on the right
implies that $B$ is a parallelogram. The obtained results yield
the sharp upper bound for the modified BanachMazur distance to the
regular hexagon.
Keywords:convex body, geometric inequality, thickness, Minkowski space, Banach space, normed space, reduced body, BanachMazur compactum, (modified) BanachMazur distance, volume ratio Categories:52A40, 46B20 
102. CMB 2006 (vol 49 pp. 117)
A Double Triangle Operator Algebra From $SL_2(\R)$ We consider the w$^*$closed operator algebra $\cA_+$ generated
by the image of the semigroup $SL_2(\R_+)$ under a unitary representation
$\rho$ of $SL_2(\R)$ on the Hilbert~space $L_2(\R)$.
We show that $\cA_+$ is a reflexive operator algebra and
$\cA_+=\Alg\cD$ where $\cD$ is a double triangle subspace
lattice. Surprisingly, $\cA_+$ is also generated as a
w$^*$closed algebra by the image under $\rho$ of a strict
subsemigroup of $SL_2(\R_+)$.
Categories:46K50, 47L55 
103. CMB 2006 (vol 49 pp. 82)
Embeddings and Duality Theorem for Weak Classical Lorentz Spaces We characterize the weight functions
$u,v,w$ on $(0,\infty)$ such that
$$
\left(\int_0^\infty f^{*}(t)^
qw(t)\,dt\right)^{1/q}
\leq
C \sup_{t\in(0,\infty)}f^{**}_u(t)v(t),
$$
where
$$
f^{**}_u(t):=\left(\int_{0}^{t}u(s)\,ds\right)^{1}
\int_{0}^{t}f^*(s)u(s)\,ds.
$$
As an application we present a~new simple characterization of
the associate space to the space $\Gamma^ \infty(v)$, determined by the
norm
$$
\f\_{\Gamma^ \infty(v)}=\sup_{t\in(0,\infty)}f^{**}(t)v(t),
$$
where
$$
f^{**}(t):=\frac1t\int_{0}^{t}f^*(s)\,ds.
$$
Keywords:Discretizing sequence, antidiscretization, classical Lorentz spaces, weak Lorentz spaces, embeddings, duality, Hardy's inequality Categories:26D10, 46E20 
104. CMB 2005 (vol 48 pp. 607)
Toeplitz Algebras and Extensions of\\Irrational Rotation Algebras For a given irrational number $\theta$, we define Toeplitz operators with
symbols in the irrational rotation algebra ${\mathcal A}_\theta$,
and we show that the $C^*$algebra $\mathcal T({\mathcal
A}_\theta)$ generated by these Toeplitz operators is an extension
of ${\mathcal A}_\theta$ by the algebra of compact operators. We
then use these extensions to explicitly exhibit generators of the
group $KK^1({\mathcal A}_\theta,\mathbb C)$. We also prove an
index theorem for $\mathcal T({\mathcal A}_\theta)$ that
generalizes the standard index theorem for Toeplitz operators on
the circle.
Keywords:Toeplitz operators, irrational rotation algebras, index theory Categories:47B35, 46L80 
105. CMB 2005 (vol 48 pp. 481)
Exact Filling of Figures with the Derivatives of Smooth Mappings Between Banach Spaces We establish sufficient conditions on the shape of a set $A$
included in the space $\mathcal L _s^n(X,Y)$ of the $n$linear
symmetric mappings between Banach spaces $X$ and $Y$, to ensure
the existence of a $C^n$\nobreakdashsmooth
mapping $f\colon X \rightarrow Y$,
with bounded support, and such that $f^{(n)}(X)=A$, provided that
$X$ admits a $C^{n}$smooth bump with bounded $n$th derivative
and $\dens X=\dens \mathcal L ^n(X,Y)$. For instance, when $X$ is
infinitedimensional, every bounded connected and open set $U$
containing the origin is the range of the $n$th derivative of
such a mapping. The same holds true for the closure of $U$,
provided that every point in the boundary of $U$ is the end
point of a path within $U$. In the finitedimensional case, more
restrictive conditions are required. We also study the Fr\'echet
smooth case for mappings from $\mathbb R^n$ to a separable
infinitedimensional Banach space and the G\^ateaux smooth case
for mappings defined on a separable infinitedimensional Banach
space and with values in a separable Banach space.
Category:46B20 
106. CMB 2005 (vol 48 pp. 455)
On GÃ¢teaux Differentiability of Convex Functions in WCG Spaces It is shown, using the BorweinPreiss variational principle
that for every continuous convex function $f$ on
a weakly compactly generated space $X$,
every $x_0\in X$ and every weakly compact convex symmetric set $K$ such that
$\cspan K=X$,
there is a point of G\^ateaux differentiability of $f$ in $x_0+K$.
This extends a Klee's result for separable spaces.
Keywords:GÃ¢teaux smoothness, BorweinPreiss variational principle,, weakly compactly generated spaces Category:46B20 
107. CMB 2005 (vol 48 pp. 340)
Short Geodesics of Unitaries in the $L^2$ Metric Let $\M$ be a type II$_1$ von Neumann algebra, $\tau$ a trace in $\M$,
and $\l2$ the GNS Hilbert space of $\tau$. We regard the unitary group
$U_\M$ as a subset of $\l2$ and characterize the shortest smooth
curves joining two fixed unitaries in the $L^2$ metric. As a
consequence of this we obtain that $U_\M$, though a complete (metric)
topological group, is not an embedded riemannian submanifold of $\l2$
Keywords:unitary group, short geodesics, infinite dimensional riemannian manifolds. Categories:46L51, 58B10, 58B25 
108. CMB 2005 (vol 48 pp. 251)
The Index Theory Associated to a NonFinite Trace on a $C^\ast$Algebra The index theory considered in this paper, a
generalisation of the classical Fredholm index theory, is obtained
in terms of a nonfinite trace on a unital $C^\ast$algebra. We relate
it to the index theory of M.~Breuer, which is developed in a
von~Neumann algebra setting, by means of a representation theorem.
We show how our new index theory can be used to obtain an index
theorem for Toeplitz operators on the compact group $\mathbf{U}(2)$,
where the classical index theory does not give any interesting result.
Categories:46L, 47B35, 47L80 
109. CMB 2005 (vol 48 pp. 283)
Enlarged Inclusion of Subdifferentials This paper studies the integration of inclusion of subdifferentials. Under
various verifiable conditions, we obtain that if two proper lower
semicontinuous functions $f$ and $g$ have the subdifferential of $f$
included in the $\gamma$enlargement of the subdifferential of $g$, then
the difference of those functions is $ \gamma$Lipschitz over their
effective domain.
Keywords:subdifferential,, directionally regular function,, approximate convex function,, subdifferentially and directionally stable function Categories:49J52, 46N10, 58C20 
110. CMB 2005 (vol 48 pp. 161)
Hankel Convolution Operators on Spaces of Entire Functions of Finite Order In this paper we study Hankel transforms and Hankel convolution
operators on spaces of entire functions of finite order and their
duals.
Keywords:Hankel transform, convolution, entire functions, finite order Category:46F12 
111. 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 
112. CMB 2005 (vol 48 pp. 69)
Biorthogonal Systems in Weakly LindelÃ¶f Spaces We study countable splitting of Markushevich bases in weakly Lindel\"of
Banach spaces in connection with the geometry of these spaces.
Keywords:Weak compactness, projectional resolutions,, Markushevich bases, Eberlein compacts, Va\v sÃ¡k spaces Categories:46B03, 46B20., 46B26 
113. 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 
114. 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

115. 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 
116. 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 
117. 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 
118. 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 
119. 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 
120. 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 
121. 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

122. 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 
123. 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 
124. 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 
125. 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 