Expand all Collapse all  Results 176  193 of 193 
176. 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 
177. 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 
178. 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 
179. 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 
180. 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 
181. 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 
182. 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 
183. 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 
184. CMB 1998 (vol 41 pp. 225)
Mazur intersection properties for compact and weakly compact convex sets Various authors have studied when a Banach space can be renormed so
that every weakly compact convex, or less restrictively every
compact convex set is an intersection of balls. We first observe
that each Banach space can be renormed so that every weakly compact
convex set is an intersection of balls, and then we introduce and
study properties that are slightly stronger than the preceding two
properties respectively.
Categories:46B03, 46B20, 46A55 
185. CMB 1998 (vol 41 pp. 41)
On the Clarke subdifferential of an integral functional on $L_p$, $1\leq p < \infty$ Given an integral functional defined on $L_p$, $1 \leq p <\infty$,
under a growth condition we give an upper bound of the Clarke
directional derivative and we obtain a nice inclusion between the
Clarke subdifferential of the integral functional and the set of
selections of the subdifferential of the integrand.
Keywords:Integral functional, integrand, epiderivative Categories:28A25, 49J52, 46E30 
186. CMB 1997 (vol 40 pp. 443)
Reflective Representations and Banach C*Modules Suppose ${\cal A}$ is a unital $C$*algebra and $m\colon{\cal A}\to B(X)$
Categories:47D30, 46L99 
187. CMB 1997 (vol 40 pp. 488)
CaractÃ©risations spectrales du radical et du socle d'une paire de jordanbanach If $f$ and $g$ are two analytic functions from a domain $D$ of the
complex plane into respectively the Banach spaces $V^+$ and $V^$,
we prove that $\lambda\mapsto \Sp\bigl(f(\lambda),g(\lambda)\bigr)$ is an
analytic multivalued function. From this derives the subharmonicity of the
functions $\lambda\mapsto \rho_V\bigl(f(\lambda),g(\lambda)\bigr)$
and $\lambda\mapsto \log\rho_V\bigl(f(\lambda),g(\lambda)\bigr)$ where
$\rho$ denotes the spectral radius. We apply these results to obtain nice
caracterizations of the radical and the socle of a Banach Jordan pair,
and finally we get an algebraic structural theorem.
Keywords:Spectre, rayon spectral, multifonction analytique, quasiinverse,, paire de JordanBanach, radical de Jacobson, socle. Categories:46H70, (17A15) 
188. CMB 1997 (vol 40 pp. 356)
Principe du maximum et lemme de Schwarz, a valeurs vectorielles Nous {\'e}tablissons un
th{\'e}or{\`e}me pour les fonctions holomorphes {\`a} valeurs dans une
partie convexe ferm{\'e}e. Ce th{\'e}or{\`e}me pr{\'e}cise
la position des coefficients de Taylor de telles fonctions et peut
{\^e}tre consid{\'e}r{\'e} comme une g{\'e}n{\'e}ralisation des
in{\'e}galit{\'e}s de Cauchy. Nous montrons alors comment ce
th{\'e}or{\`e}me permet de retrouver des versions connues du principe
du maximum et d'obtenir de nouveaux r{\'e}sultats sur les
applications holomorphes {\`a} valeurs vectorielles.
Keywords:Principe du maximum, lemme de Schwarz, points extr{Ã©maux. Categories:30C80, 32A30, 46G20, 52A07 
189. CMB 1997 (vol 40 pp. 129)
Sur les caractÃ¨res d'une algÃ¨bre de Banach A new proof for the GleasonKahane\.Zelazko theorem concerning the
characters of a Banach algebra is given. A theorem due to P\'olya and
Saxer is used instead of the Hadamard factorization theorem.
Categories:46H05, 32A15 
190. CMB 1997 (vol 40 pp. 254)
Subdiagonal algebras for subfactors II (finite dimensional case) We show that finite dimensional subfactors do not have subdiagonal
algebras unless the Jones index is one.
Categories:46K50, 46L37 
191. CMB 1997 (vol 40 pp. 183)
The range of group algebra homomorphisms A characterisation of the range of a homomorphism between two
commutative group algebras is presented which implies, among other
things, that this range is closed. The work relies mainly on the
characterisation of such homomorphisms achieved by P.~J.~Cohen.
Categories:43A22, 22B10, 46J99 
192. CMB 1997 (vol 40 pp. 133)
Derivations from totally ordered semigroup algebras into their duals For a wellbehaved measure $\mu$, on a locally compact
totally ordered set $X$, with continuous part $\mu_c$, we make
$L^p(X,\mu_c)$
into a commutative Banach bimodule over the totally ordered
semigroup algebra
$L^p(X,\mu)$, in such a way that the natural surjection from the algebra
to the module is a bounded derivation. This gives rise to bounded
derivations from $L^p(X,\mu)$
into its dual module and in particular shows that if $\mu_c$ is not
identically zero then $L^p(X,\mu)$ is not weakly
amenable. We show that all bounded derivations from $L^1(X,\mu)$
into its dual module arise in this way and also describe all bounded
derivations from
$L^p(X,\mu)$ into its dual for $1

193. CMB 1997 (vol 40 pp. 10)
Convex functions on Banach spaces not containing $\ell_1$ There is a sizeable class of results precisely
relating boundedness, convergence and differentiability properties
of continuous convex functions on Banach spaces to whether or
not the space contains an isomorphic copy of $\ell_1$. In this
note, we provide constructions showing that the main such
results do not extend to natural broader classes of functions.
Categories:46A55, 46B20, 52A41 