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Weak Baire measurability of the balls in a Banach space

José Rodríguez (2008)

Studia Mathematica

Let X be a Banach space. The property (∗) “the unit ball of X belongs to Baire(X, weak)” holds whenever the unit ball of X* is weak*-separable; on the other hand, it is also known that the validity of (∗) ensures that X* is weak*-separable. In this paper we use suitable renormings of $ℓ^{\infty} (ℕ)$ and the Johnson-Lindenstrauss spaces to show that (∗) lies strictly between the weak*-separability of X* and that of its unit ball. As an application, we provide a negative answer to a question raised by K. Musiał....

Weak Cauchy sequences in $L_{\infty} (μ, X)$

Georg Schlüchtermann (1995)

Studia Mathematica

For a finite and positive measure space Ω,∑,μ characterizations of weak Cauchy sequences in $L_{\infty} (μ, X)$ , the space of μ-essentially bounded vector-valued functions f:Ω → X, are presented. The fine distinction between Asplund and conditionally weakly compact subsets of $L_{\infty} (μ, X)$ is discussed.

Weak compactness criteria for set valued integrals and Radon Nikodym Theorem for vector valued multimeasures

Diomedes Bárcenas (2001)

Czechoslovak Mathematical Journal

Some criteria for weak compactness of set valued integrals are given. Also we show some applications to the study of multimeasures on Banach spaces with the Radon-Nikodym property.

Weak compactness in the space of operator valued measures $M_{b} a (Σ, (X, Y))$ and its applications

N.U. Ahmed (2011)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this note we present necessary and sufficient conditions characterizing conditionally weakly compact sets in the space of (bounded linear) operator valued measures $M_{b a} (Σ, (X, Y))$ . This generalizes a recent result of the author characterizing conditionally weakly compact subsets of the space of nuclear operator valued measures $M_{b a} (Σ, ₁ (X, Y))$ . This result has interesting applications in optimization and control theory as illustrated by several examples.

Weak compactness of unconditionally convergent operators on $C_{0} (T)$

Thiruvaiyaru V. Panchapagesan (2002)

Mathematica Slovaca

Weak continuity of holomorphic automorphisms in JB-triples.

Wilhelm Kaup, José M. Isidro (1992)

Mathematische Zeitschrift

Weak Convergence of Measures.

Helmut H. SCHAEFER (1971)

Mathematische Annalen

Weak Convergence of Vector Measures on F-Space.

Tsang-hai Kuo (1975)

Mathematische Zeitschrift

Weak Fubini theorems for the Dobrakov integral

Charles W. Swartz (1980)

Czechoslovak Mathematical Journal

Weak meromorphic extension

L. Hai, N. Khue, N. Nga (1993)

Colloquium Mathematicae

Weak* sequential compactness and bornological limit derivatives.

Borwein, Jonathan, Fitzpatrick, Simon (1995)

Journal of Convex Analysis

Weaker forms of continuity and vector-valued Riemann integration

M. A. Sofi (2012)

Colloquium Mathematicae

It was proved by Kadets that a weak*-continuous function on [0,1] taking values in the dual of a Banach space X is Riemann-integrable precisely when X is finite-dimensional. In this note, we prove a Fréchet-space analogue of this result by showing that the Riemann integrability holds exactly when the underlying Fréchet space is Montel.

Weakly compact operators and $u$ -additive measures

José Aguayo-Garrido, Miguel Nova-Yañez (2000)

Annales mathématiques Blaise Pascal

Weakly precompact subsets of L₁(μ,X)

Ioana Ghenciu (2012)

Colloquium Mathematicae

Let (Ω,Σ,μ) be a probability space, X a Banach space, and L₁(μ,X) the Banach space of Bochner integrable functions f:Ω → X. Let W = f ∈ L₁(μ,X): for a.e. ω ∈ Ω, ||f(ω)|| ≤ 1. In this paper we characterize the weakly precompact subsets of L₁(μ,X). We prove that a bounded subset A of L₁(μ,X) is weakly precompact if and only if A is uniformly integrable and for any sequence (fₙ) in A, there exists a sequence (gₙ) with $g ₙ \in c o f_{i} : i \geq n$ for each n such that for a.e. ω ∈ Ω, the sequence (gₙ(ω)) is weakly Cauchy in X....

Weierstrass' theorem in weighted Sobolev spaces with $k$ derivatives: announcement of results.

Portilla, Ana, Quintana, Yamilet, Rodriguez, Jose M., Touris, Eva (2006)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

When does finite holomorphy imply holomorphy?

Nachbin, Leopoldo (1994)

Portugaliae Mathematica

When some variational properties force convexity

M. Volle, J.-B. Hiriart-Urruty, C. Zălinescu (2013)

ESAIM: Control, Optimisation and Calculus of Variations

The notion of adequate (resp. strongly adequate) function has been recently introduced to characterize the essentially strictly convex (resp. essentially firmly subdifferentiable) functions among the weakly lower semicontinuous (resp. lower semicontinuous) ones. In this paper we provide various necessary and sufficient conditions in order that the lower semicontinuous hull of an extended real-valued function on a reflexive Banach space is essentially strictly convex. Some new results on nearest...

Wiener integral for the coordinate process under the σ-finite measure unifying Brownian penalisations

Kouji Yano (2011)

ESAIM: Probability and Statistics

Wiener integral for the coordinate process is defined under the σ-finite measure unifying Brownian penalisations, which has been introduced by [Najnudel et al., C. R. Math. Acad. Sci. Paris345 (2007) 459–466] and [Najnudel et al., MSJ Memoirs19. Mathematical Society of Japan, Tokyo (2009)]. Its decomposition before and after last exit time from 0 is studied. This study prepares for the author's recent study [K. Yano, J. Funct. Anal.258 (2010) 3492–3516] of Cameron-Martin formula for the...

Wiener integral for the coordinate process under the σ-finite measure unifying brownian penalisations

Kouji Yano (2011)

ESAIM: Probability and Statistics

Wiener integral for the coordinate process is defined under the σ-finite measure unifying Brownian penalisations, which has been introduced by [Najnudel et al., C. R. Math. Acad. Sci. Paris 345 (2007) 459–466] and [Najnudel et al., MSJ Memoirs 19. Mathematical Society of Japan, Tokyo (2009)]. Its decomposition before and after last exit time from 0 is studied. This study prepares for the author's recent study [K. Yano, J. Funct. Anal. 258 (2010) 3492–3516] of Cameron-Martin formula for the σ-finite...

Wiener integral in the space of sequences of real numbers

Alexandre de Andrade, Paulo R. C. Ruffino (2000)

Archivum Mathematicum

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