Expand all Collapse all  Results 151  175 of 185 
151. 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 
152. 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 
153. 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 
154. 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 $2^{n1}$ metric
equalities.
Keywords:normed spaces, hypercubes Categories:46B04, 05C10, 05B99 
155. 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 
156. 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 
157. 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 
158. CMB 2000 (vol 43 pp. 320)
On Classification of Certain $C^\ast$Algebras We consider \cstalgebras which are inductive limits of finite
direct sums of copies of $ C([0,1]) \otimes \Otwo$. For such
algebras, the lattice of closed twosided ideals is proved to be
a complete invariant.
Categories:46L05, 46L35 
159. CMB 2000 (vol 43 pp. 368)
KahaneKhinchin's Inequality for QuasiNorms We extend the recent results of R.~Lata{\l}a and O.~Gu\'edon about
equivalence of $L_q$norms of logconcave random variables
(KahaneKhinchin's inequality) to the quasiconvex case. We
construct examples of quasiconvex bodies $K_n \subset \R$ which
demonstrate that this equivalence fails for uniformly distributed
vector on $K_n$ (recall that the uniformly distributed vector on a
convex body is logconcave). Our examples also show the lack of the
exponential decay of the ``tail" volume (for convex bodies such
decay was proved by M.~Gromov and V.~Milman).
Categories:46B09, 52A30, 60B11 
160. CMB 2000 (vol 43 pp. 257)
161. CMB 2000 (vol 43 pp. 193)
C$^*$Convexity and the Numerical Range If $A$ is a prime C$^*$algebra, $a \in A$ and $\lambda$ is in the
numerical range $W(a)$ of $a$, then for each $\varepsilon > 0$ there
exists an element $h \in A$ such that $\norm{h} = 1$ and $\norm{h^*
(a\lambda)h} < \varepsilon$. If $\lambda$ is an extreme point of
$W(a)$, the same conclusion holds without the assumption that $A$ is
prime. Given any element $a$ in a von Neumann algebra (or in a
general C$^*$algebra) $A$, all normal elements in the weak* closure
(the norm closure, respectively) of the C$^*$convex hull of $a$ are
characterized.
Categories:47A12, 46L05, 46L10 
162. CMB 2000 (vol 43 pp. 208)
Extensions of Continuous and Lipschitz Functions We show a result slightly more general than the following. Let $K$
be a compact Hausdorff space, $F$ a closed subset of $K$, and $d$ a
lower semicontinuous metric on $K$. Then each continuous function
$f$ on $F$ which is Lipschitz in $d$ admits a continuous extension on
$K$ which is Lipschitz in $d$. The extension has the same supremum
norm and the same Lipschitz constant.
As a corollary we get that a Banach space $X$ is reflexive if and only
if each bounded, weakly continuous and norm Lipschitz function
defined on a weakly closed subset of $X$ admits a weakly continuous,
norm Lipschitz extension defined on the entire space $X$.
Keywords:extension, continous, Lipschitz, Banach space Categories:54C20, 46B10 
163. CMB 2000 (vol 43 pp. 138)
Exponential Laws for the Nachbin Ported Topology We show that for $U$ and $V$ balanced open subsets of (Qno) Fr\'echet
spaces $E$ and $F$ that we have the topological identity
$$
\bigl( {\cal H}(U\times V), \tau_\omega \bigr) = \biggl( {\cal H}
\Bigl( U; \bigl( {\cal H}(V), \tau_\omega \bigr) \Bigr), \tau_\omega
\biggr).
$$
Analogous results for the compact open topology have long been
established. We also give an example to show that the (Qno)
hypothesis on both $E$ and $F$ is necessary.
Categories:46G20, 18D15, 46M05 
164. CMB 2000 (vol 43 pp. 69)
Type II Spectral Flow and the Eta Invariant The relative eta invariant of AtiyahPatodiSinger will be shown to be
expressible in terms of the notion of Type~I and Type~II spectral flow.
Categories:19K56, 46L80 
165. CMB 1999 (vol 42 pp. 344)
Positive Definite Distributions and Subspaces of $L_p$ With Applications to Stable Processes We define embedding of an $n$dimensional normed space into
$L_{p}$, $0

166. CMB 1999 (vol 42 pp. 321)
Averaging Operators and Martingale Inequalities in Rearrangement Invariant Function Spaces We shall study some connection between averaging operators and
martingale inequalities in rearrangement invariant function spaces.
In Section~2 the equivalence between Shimogaki's theorem and some
martingale inequalities will be established, and in Section~3 the
equivalence between Boyd's theorem and martingale inequalities with
change of probability measure will be established.
Keywords:martingale inequalities, rearrangement invariant function spaces Categories:60G44, 60G46, 46E30 
167. CMB 1999 (vol 42 pp. 274)
The Bockstein Map is Necessary We construct two nonisomorphic nuclear, stably finite,
real rank zero $C^\ast$algebras $E$ and $E'$ for which
there is an isomorphism of ordered groups
$\Theta\colon \bigoplus_{n \ge 0} K_\bullet(E;\ZZ/n) \to
\bigoplus_{n \ge 0} K_\bullet(E';\ZZ/n)$ which is compatible
with all the coefficient transformations. The $C^\ast$algebras
$E$ and $E'$ are not isomorphic since there is no $\Theta$
as above which is also compatible with the Bockstein operations.
By tensoring with Cuntz's algebra $\OO_\infty$ one obtains a pair
of nonisomorphic, real rank zero, purely infinite $C^\ast$algebras
with similar properties.
Keywords:$K$theory, torsion coefficients, natural transformations, Bockstein maps, $C^\ast$algebras, real rank zero, purely infinite, classification Categories:46L35, 46L80, 19K14 
168. CMB 1999 (vol 42 pp. 139)
Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions 
Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions Every weakly compact composition operator between weighted Banach
spaces $H_v^{\infty}$ of analytic functions with weighted supnorms is
compact. Lower and upper estimates of the essential norm of
continuous composition operators are obtained. The norms of the point
evaluation functionals on the Banach space $H_v^{\infty}$ are also
estimated, thus permitting to get new characterizations of compact
composition operators between these spaces.
Keywords:weighted Banach spaces of holomorphic functions, composition operator, compact operator, weakly compact operator Categories:47B38, 30D55, 46E15 
169. CMB 1999 (vol 42 pp. 221)
Boundedness of the $q$MeanSquare Operator on VectorValued Analytic Martingales We study boundedness properties of the $q$meansquare operator
$S^{(q)}$ on $E$valued analytic martingales, where $E$ is a
complex quasiBanach space and $2 \leq q < \infty$. We establish
that a.s. finiteness of $S^{(q)}$ for every bounded $E$valued
analytic martingale implies strong $(p,p)$type estimates for
$S^{(q)}$ and all $p\in (0,\infty)$. Our results yield new
characterizations (in terms of analytic and stochastic properties
of the function $S^{(q)}$) of the complex spaces $E$ that admit an
equivalent $q$uniformly PLconvex quasinorm. We also obtain a
vectorvalued extension (and a characterization) of part of an
observation due to Bourgain and Davis concerning the
$L^p$boundedness of the usual squarefunction on scalarvalued
analytic martingales.
Categories:46B20, 60G46 
170. CMB 1999 (vol 42 pp. 118)
Points of Weak$^\ast$Norm Continuity in the Unit Ball of the Space $\WC(K,X)^\ast$ For a compact Hausdorff space with a dense set of isolated points, we
give a complete description of points of weak$^\ast$norm continuity
in the dual unit ball of the space of Banach space valued functions
that are continuous when the range has the weak topology. As an
application we give a complete description of points of weaknorm
continuity of the unit ball of the space of vector measures when
the underlying Banach space has the RadonNikodym property.
Keywords:Points of weak$^\ast$norm continuity, space of vector valued weakly continuous functions, $M$ideals Categories:46B20, 46E40 
171. CMB 1999 (vol 42 pp. 104)
InstabilitÃ© de vecteurs propres d'opÃ©rateurs linÃ©aires We consider some geometric properties of eigenvectors of linear
operators on infinite dimensional Hilbert space. It is proved that
the property of a family of vectors $(x_n)$ to be eigenvectors
$Tx_n= \lambda_n x_n$ ($\lambda_n \noteq \lambda_k$ for $n\noteq k$)
of a bounded operator $T$ (admissibility property) is very instable
with respect to additive and linear perturbations. For instance,
(1)~for the sequence $(x_n+\epsilon_n v_n)_{n\geq k(\epsilon)}$ to
be admissible for every admissible $(x_n)$ and for a suitable
choice of small numbers $\epsilon_n\noteq 0$ it is necessary and
sufficient that the perturbation sequence be eventually scalar:
there exist $\gamma_n\in \C$ such that $v_n= \gamma_n v_{k}$ for
$n\geq k$ (Theorem~2); (2)~for a bounded operator $A$ to transform
admissible families $(x_n)$ into admissible families $(Ax_n)$ it is
necessary and sufficient that $A$ be left invertible (Theorem~4).
Keywords:eigenvectors, minimal families, reproducing kernels Categories:47A10, 46B15 
172. CMB 1998 (vol 41 pp. 279)
New characterizations of the reflexivity in terms of the set of norm attaining functionals As a consequence of results due to Bourgain and Stegall, on a
separable Banach space whose unit ball is not dentable, the
set of norm attaining functionals has empty interior (in the
norm topology). First we show that any Banach space can be renormed to
fail this property. Then, our main positive result can be stated as
follows: if a separable Banach space $X$ is very smooth or its bidual
satisfies the $w^{\ast }$Mazur intersection property, then either $X$
is reflexive or the set of norm attaining functionals has empty
interior, hence the same result holds if $X$ has the Mazur
intersection property and so, if the norm of $X$ is Fr\'{e}chet
differentiable. However, we prove that smoothness is not a sufficient
condition for the same conclusion.
Categories:46B04, 46B10, 46B20 
173. CMB 1998 (vol 41 pp. 257)
Note on the support of Sobolev functions We prove a topological restriction on the support of Sobolev functions.
Categories:46E35, 31B05 
174. CMB 1998 (vol 41 pp. 145)
Smooth partitions of unity on Banach spaces It is shown that if a Banach space $X$ admits a $C^k$smooth bump
function, and $X^{*}$ is Asplund, then $X$ admits $C^k$smooth
partitions of unity.
Category:46B20 
175. CMB 1998 (vol 41 pp. 240)
On certain $K$groups associated with minimal flows It is known that the Toeplitz algebra associated with any flow
which is both minimal and uniquely ergodic always has a trivial
$K_1$group. We show in this note that if the unique ergodicity is
dropped, then such $K_1$group can be nontrivial. Therefore, in
the general setting of minimal flows, even the $K$theoretical
index is not sufficient for the classification of Toeplitz
operators which are invertible modulo the commutator ideal.
Categories:46L80, 47B35, 47C15 