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Weak bases in $p$ -adic spaces

N. De Grande-De Kimpe, J. Kąkol, C. Perez-Garcia, W. H. Schikhof (2002)

Bollettino dell'Unione Matematica Italiana

We study polar locally convex spaces over a non-archimedean non-trivially valued complete field with a weak topological basis. We prove two completeness theorems and a Hahn-Banach type theorem for locally convex spaces with a weak Schauder basis.

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 and summability

Wojciech Chojnacki (1987)

Mathematica Slovaca

Weak compactness criteria and convergences in LE1(μ).

H. Benabdellah, C. Castaing (1997)

Collectanea Mathematica

Weak Compactness in Locally Convex g-Spaces and Related Questions.

Stanislav TOMÁSEK (1971)

Mathematische Annalen

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 Multiplication Operators on Spaces of Bounded Linear Operators.

Eero Saksman, Hans-Olav Tylli (1992)

Mathematica Scandinavica

Weak Compactness, Pseudo-reflexivity and Quasi-reflexivity.

I. SINGER (1964)

Mathematische Annalen

Weak convergence in infinite dimensional spaces

Jan Franců (1994)

Acta Mathematica et Informatica Universitatis Ostraviensis

Weak countable compactness implies quasi-weak drop property

J. H. Qiu (2004)

Studia Mathematica

Every weakly countably compact closed convex set in a locally convex space has the quasi-weak drop property.

Weak Grothendieck's theorem.

Mezrag, Lahcène (2006)

International Journal of Mathematics and Mathematical Sciences

Weak $^{*}$ -norm sequentially continuous operators

Alimohammady Mohsen (2000)

Mathematica Slovaca

Weak orthogonality and weak property ( $β$ ) in some Banach sequence spaces

Yunan Cui, Henryk Hudzik, Ryszard Płuciennik (1999)

Czechoslovak Mathematical Journal

It is proved that a Köthe sequence space is weakly orthogonal if and only if it is order continuous. Criteria for weak property ( $β$ ) in Orlicz sequence spaces in the case of the Luxemburg norm as well as the Orlicz norm are given.

Weak* sequential compactness and bornological limit derivatives.

Borwein, Jonathan, Fitzpatrick, Simon (1995)

Journal of Convex Analysis

Weak sequential completeness of sequence spaces.

Charles Swartz (1992)

Collectanea Mathematica

Köthe and Toeplitz introduced the theory of sequence spaces and established many of the basic properties of sequence spaces by using methods of classical analysis. Later many of these same properties of sequence spaces were reestablished by using soft proofs of functional analysis. In this note we would like to point out that an improved version of a classical lemma of Schur due to Hahn can be used to give very short proofs of two of the weak sequential completeness results of Köthe and Toeplitz....

Weak Topology in Locally Convex Spaces With a Fundamental Sequence of Bounded Sets

Stojan Radenović, Zoran Kadelburg (1997)

Matematički Vesnik

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.

Currently displaying 1 – 20 of 33