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Gateaux Differentiability of Convex Functions and Topology: Weak Asplund Spaces (Chemical Analysis)by Marian J. Fabian
Synopses & Reviews
This text puts together "folklore results" touching weak Asplund spaces. It presents a thorough examination of weak Asplund cases. Nonseparable Banach spaces, renorming, and differentiability are stressed throughout the text and all subclasses, including inferences and counterexamples are discussed. It also covers Stegall's classes, fragmentability, and "long sequences" of linear projections. Notes, remarks and questions end each chapter.
Book News Annotation:
Presents results and the many open questions related to weak Asplund spaces, which unlike their stronger siblings, have proven elusive and difficult to study. Discusses Asplund spaces, Asplund generated spaces, weakly compactly generated spaces, Vasak spaces, and Banach spaces whose dual belong to Stegall's class, and the relations between them. Also considers various classes of topological spaces, include Eberlein, Gul'ko, Radon-Nikodym compacta, and fragmentabilty. For functional analysts working with nonseparable Banach spaces and differentiability.
Annotation c. Book News, Inc., Portland, OR (booknews.com)
Table of Contents
Canonical Examples of Weak Asplund Spaces.
Properties of Gateaux Differentiability Spaces and Weak Asplund Spaces.
Two More Concrete Classes of Banach Spaces that Lie in .
"Long Sequences" of Linear Projections.
Vaak Spaces and Gul'ko Compacta.
A Characterization of WCG Spaces and of Eberlein Compacta.
Main Open Questions and Problems.
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