Expand all Collapse all | Results 126 - 150 of 178 |
126. 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 |
127. 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 |
128. CMB 2003 (vol 46 pp. 419)
On Non-Strongly Free Automorphisms of Subfactors of Type III$_0$ We determine when an automorphism of a subfactor of type III$_0$
with finite index is non-strongly free in the sense of C.~Winsl\o w
in terms of the modular endomorphisms introduced by M.~Izumi.
Category:46L37 |
129. 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 |
130. CMB 2003 (vol 46 pp. 441)
An Inductive Limit Model for the $K$-Theory of the Generator-Interchanging Antiautomorphism of an Irrational Rotation Algebra |
An Inductive Limit Model for the $K$-Theory of the Generator-Interchanging 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 |
131. 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 |
132. 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 |
133. CMB 2003 (vol 46 pp. 164)
Classification of $\AF$ Flows An $\AF$ flow is a one-parameter 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/path-space construction, and one in terms of a modified
$K_0$ functor.
Categories:46L57, 46L35 |
134. 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 |
135. 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 |
136. 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
non-unital endomorphism of the multiplier algebra), and has range an
ideal of $A$. We show that there is a partial action on the fixed-point
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 |
137. CMB 2003 (vol 46 pp. 80)
Multi-Sided Braid Type Subfactors, II We show that the multi-sided inclusion $R^{\otimes l} \subset R$ of
braid-type subfactors of the hyperfinite II$_1$ factor $R$, introduced
in {\it Multi-sided braid type subfactors} [E3], contains a sequence
of intermediate subfactors: $R^{\otimes l} \subset R^{\otimes l-1}
\subset \cdots \subset R^{\otimes 2} \subset R$. That is, every
$t$-sided subfactor is an intermediate subfactor for the inclusion
$R^{\otimes l} \subset R$, for $2\leq t\leq l$. Moreover, we also
show that if $t>m$ then $R^{\otimes t} \subset R^{\otimes m}$ is
conjugate to $R^{\otimes t-m+1} \subset R$. Thus, if the braid
representation considered is associated to one of the classical Lie
algebras then the asymptotic inclusions for the Jones-Wenzl subfactors
are intermediate subfactors.
Category:46L37 |
138. CMB 2002 (vol 45 pp. 321)
$C^{\ast}$-Algebras of Infinite Graphs and Cuntz-Krieger Algebras The Cuntz-Krieger algebra $\mathcal{O}_B$ is defined for an
arbitrary, possibly infinite and infinite valued, matrix $B$. A graph
$C^{\ast}$-algebra $G^{\ast} (E)$ is introduced for an arbitrary
directed graph $E$, and is shown to coincide with a previously defined
graph algebra $C^{\ast} (E)$ if each source of $E$ emits only finitely
many edges. Each graph algebra $G^{\ast} (E)$ is isomorphic to the
Cuntz-Krieger algebra $\mathcal{O}_B$ where $B$ is the vertex matrix
of~$E$.
Categories:46LXX, 05C50 |
139. CMB 2002 (vol 45 pp. 232)
On Strongly Convex Indicatrices in Minkowski Geometry The geometry of indicatrices is the foundation of Minkowski geometry.
A strongly convex indicatrix in a vector space is a strongly convex
hypersurface. It admits a Riemannian metric and has a distinguished
invariant---(Cartan) torsion. We prove the existence of non-trivial
strongly convex indicatrices with vanishing mean torsion and discuss
the relationship between the mean torsion and the Riemannian curvature
tensor for indicatrices of Randers type.
Categories:46B20, 53C21, 53A55, 52A20, 53B40, 53A35 |
140. CMB 2002 (vol 45 pp. 309)
Joint Mean Oscillation and Local Ideals in the Toeplitz Algebra II: Local Commutivity and Essential Commutant |
Joint Mean Oscillation and Local Ideals in the Toeplitz Algebra II: Local Commutivity and Essential Commutant A well-known theorem of Sarason [11] asserts that if $[T_f,T_h]$ is
compact for every $h \in H^\infty$, then $f \in H^\infty + C(T)$.
Using local analysis in the full Toeplitz algebra $\calT = \calT
(L^\infty)$, we show that the membership $f \in H^\infty + C(T)$ can
be inferred from the compactness of a much smaller collection of
commutators $[T_f,T_h]$. Using this strengthened result and a theorem
of Davidson [2], we construct a proper $C^\ast$-subalgebra $\calT
(\calL)$ of $\calT$ which has the same essential commutant as that of
$\calT$. Thus the image of $\calT (\calL)$ in the Calkin algebra does
not satisfy the double commutant relation [12], [1]. We will also
show that no {\it separable} subalgebra $\calS$ of $\calT$ is capable
of conferring the membership $f \in H^\infty + C(T)$ through the
compactness of the commutators $\{[T_f,S] : S \in \calS\}$.
Categories:46H10, 47B35, 47C05 |
141. CMB 2002 (vol 45 pp. 265)
On the Smirnov Class Defined by the Maximal Function H.~O.~Kim has shown that contrary to the case of
$H^p$-space, the Smirnov class $M$ defined by the radial maximal
function is essentially smaller than the classical Smirnov class
of the disk. In the paper we show that these two classes have the
same corresponding locally convex structure, {\it i.e.} they have the
same dual spaces and the same Fr\'echet envelopes. We describe a
general form of a continuous linear functional on $M$ and
multiplier from $M$ into $H^p$, $0 < p \leq \infty$.
Keywords:Smirnov class, maximal radial function, multipliers, dual space, FrÃ©chet envelope Categories:46E10, 30A78, 30A76 |
142. CMB 2002 (vol 45 pp. 3)
Real-Analytic Negligibility of Points and Subspaces in Banach Spaces, with Applications We prove that every infinite-dimensional Banach space $X$ having a
(not necessarily equivalent) real-analytic norm is real-analytic
diffeomorphic to $X \setminus \{0\}$. More generally, if $X$ is an
infinite-dimensional Banach space and $F$ is a closed subspace of $X$
such that there is a real-analytic seminorm on $X$ whose set of zeros
is $F$, and $X/F$ is infinite-dimensional, then $X$ and $X \setminus
F$ are real-analytic diffeomorphic. As an application we show the
existence of real-analytic free actions of the circle and the
$n$-torus on certain Banach spaces.
Categories:46B20, 58B99 |
143. CMB 2002 (vol 45 pp. 60)
Uniform Embeddings into Hilbert Space and a Question of Gromov Gromov introduced the concept of uniform embedding into Hilbert space
and asked if every separable metric space admits a uniform embedding
into Hilbert space. In this paper, we study uniform embedding into
Hilbert space and answer Gromov's question negatively.
Category:46C05 |
144. CMB 2002 (vol 45 pp. 46)
Local $\VMO$ and Weak Convergence in $\hone$ A local version of $\VMO$ is defined, and the local Hardy space
$\hone$ is shown to be its dual. An application to weak-$*$
convergence in $\hone$ is proved.
Categories:42B30, 46E99 |
145. CMB 2001 (vol 44 pp. 504)
Weak Amenability of a Class of Banach Algebras We show that, if a Banach algebra $\A$ is a left ideal in its second
dual algebra and has a left bounded approximate identity, then the
weak amenability of $\A$ implies the ($2m+1$)-weak amenability of $\A$
for all $m\geq 1$.
Keywords:$n$-weak amenability, left ideals, left bounded approximate identity Categories:46H20, 46H10, 46H25 |
146. CMB 2001 (vol 44 pp. 355)
Hilbert Bimodules with Involution We examine Hilbert bimodules which possess a (generally unbounded)
involution. Topics considered include a linking algebra
representation, duality, locality, and the role of these bimodules
in noncommutative differential geometry
Categories:46L08, 46L57, 46L87 |
147. CMB 2001 (vol 44 pp. 370)
On Locating Isometric $\ell_{1}^{(n)}$ Motivated by a question of Per Enflo, we develop a hypercube criterion
for locating linear isometric copies of $\lone$ in an arbitrary real
normed space $X$.
The said criterion involves finding $2^{n}$ points in $X$ that satisfy
one metric equality. This contrasts nicely to the standard classical
criterion wherein one seeks $n$ points that satisfy $2^{n-1}$ metric
equalities.
Keywords:normed spaces, hypercubes Categories:46B04, 05C10, 05B99 |
148. CMB 2001 (vol 44 pp. 335)
Inductive Limit Toral Automorphisms of Irrational Rotation Algebras Irrational rotation $C^*$-algebras have an inductive limit
decomposition in terms of matrix algebras over the space of continuous
functions on the circle and this decomposition can be chosen to be
invariant under the flip automorphism. It is shown that the flip is
essentially the only toral automorphism with this property.
Categories:46L40, 46L35 |
149. CMB 2001 (vol 44 pp. 105)
Convolution Equation in $\mathcal{S}^{\prime\ast}$---Propagation of Singularities The singular spectrum of $u$ in a convolution equation $\mu * u = f$,
where $\mu$ and $f$ are tempered ultradistributions of Beurling or
Roumieau type is estimated by
$$
SS u \subset (\mathbf{R}^n \times \Char \mu) \cup SS f.
$$
The same is done for $SS_{*}u$.
Categories:32A40, 46F15, 58G07 |
150. CMB 2000 (vol 43 pp. 418)
Obstructions to $\mathcal{Z}$-Stability for Unital Simple $C^*$-Algebras Let $\cZ$ be the unital simple nuclear infinite dimensional
$C^*$-algebra which has the same Elliott invariant as $\bbC$,
introduced in \cite{JS}. A $C^*$-algebra is called $\cZ$-stable
if $A \cong A \otimes \cZ$. In this note we give some necessary
conditions for a unital simple $C^*$-algebra to be $\cZ$-stable.
Keywords:simple $C^*$-algebra, $\mathcal{Z}$-stability, weak (un)perforation in $K_0$ group, property $\Gamma$, finiteness Category:46L05 |