scholarly journals Boundaries for Banach spaces determine weak compactness

2010 ◽  
Vol 182 (3) ◽  
pp. 585-604 ◽  
Author(s):  
Hermann Pfitzner
Keyword(s):  
Banach Spaces ◽  
Weak Compactness

Weak compactness of Fréchet-derivatives: application to composition operators

1980 ◽  
Vol 29 (4) ◽  
pp. 399-406
Author(s):  
Peter Dierolf ◽  
Jürgen Voigt
Keyword(s):  
Banach Spaces ◽  
Integral Equations ◽  
Sobolev Spaces ◽  
Composition Operators ◽  
Weak Compactness ◽  
Nonlinear Integral Equations ◽  
Weakly Compact ◽  
Frechet Derivatives ◽  
Fréchet Derivatives ◽  
Compact Map

AbstractWe prove a result on compactness properties of Fréchet-derivatives which implies that the Fréchet-derivative of a weakly compact map between Banach spaces is weakly compact. This result is applied to characterize certain weakly compact composition operators on Sobolev spaces which have application in the theory of nonlinear integral equations and in the calculus of variations.

Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions

1999 ◽  
Vol 42 (2) ◽  
pp. 139-148 ◽  
Author(s):  
José Bonet ◽  
Paweł Dománski ◽  
Mikael Lindström
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Essential Norm ◽  
Weak Compactness ◽  
Weakly Compact ◽  
Point Evaluation ◽  
Weighted Banach Spaces ◽  
Spaces Of Analytic Functions

AbstractEvery weakly compact composition operator between weighted Banach spaces of analytic functions with weighted sup-norms 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 are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.

Ideal Exhaustiveness, Weak Convergence and Weak Compactness in Banach Spaces

2012 ◽  
Vol 37 (2) ◽  
pp. 389 ◽  
Author(s):  
Antonio Boccuto ◽  
Pratulananda Das ◽  
Xenofon Dimitriou ◽  
Nikolaos Papanastassiou
Keyword(s):  
Weak Convergence ◽  
Banach Spaces ◽  
Weak Compactness

scholarly journals Weak compactness and σ-Asplund generated Banach spaces

2007 ◽  
Vol 181 (2) ◽  
pp. 125-152 ◽  
Author(s):  
M. Fabian ◽  
V. Montesinos ◽  
V. Zizler
Keyword(s):  
Banach Spaces ◽  
Weak Compactness

scholarly journals AN ELEMENTARY PROOF OF JAMES’ CHARACTERIZATION OF WEAK COMPACTNESS

2011 ◽  
Vol 84 (1) ◽  
pp. 98-102 ◽  
Author(s):  
WARREN B. MOORS
Keyword(s):  
Integral Representation ◽  
Banach Spaces ◽  
Elementary Proof ◽  
Weak Compactness ◽  
Representation Theorems

AbstractIn this paper we provide an elementary proof of James’ characterization of weak compactness in separable Banach spaces. The proof of the theorem does not rely upon either Simons’ inequality or any integral representation theorems. In fact the proof only requires the Krein–Milman theorem, Milman’s theorem and the Bishop–Phelps theorem.

scholarly journals A spectral radius problem connected with weak compactness

1993 ◽  
Vol 35 (1) ◽  
pp. 85-94 ◽  
Author(s):  
Hans-Olav Tylli
Keyword(s):  
Asymptotic Behaviour ◽  
Banach Spaces ◽  
Spectral Radius ◽  
Spectral Properties ◽  
Weak Compactness ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Radius Problem

The asymptotic behaviour has been determined for several natural geometric or topological quantities related to (degrees of) compactness of bounded linear operators on Banach spaces; see for instance [24], [25] and [17]. This paper complements these results by studying the spectral properties of some quantities related to weak compactness.

AN ELEMENTARY PROOF OF JAMES’ CHARACTERISATION OF WEAK COMPACTNESS. II

2016 ◽  
Vol 95 (1) ◽  
pp. 133-137 ◽  
Author(s):  
WARREN B. MOORS ◽  
SAMUEL J. WHITE
Keyword(s):  
Banach Spaces ◽  
Elementary Proof ◽  
Weak Compactness

In this paper we provide an elementary proof of James’ characterisation of weak compactness for Banach spaces whose dual ball is weak∗sequentially compact.

Sign in / Sign up

Export Citation Format

Share Document