Gâteaux Differentiability of Convex Functions and Topology

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.Dieser Band behandelt schwache Asplund-Räume, die zu Zeit Beachtung in der Literatur finden. Nichtseparable Banachräume, Renormierung und Differenzierbarkeit werden gleichermaßen diskutiert. In bemerkenswert pädagogisch wertvoller Weise führt der Autor auch den Nicht-Fachmann in die Problematik ein. Canonical Examples of Weak Asplund Spaces.

Properties of Gateaux Differentiability Spaces and Weak AsplundSpaces.

Stegall's Classes.

Two More Concrete Classes of Banach Spaces that Lie in .

Fragmentability.

"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.

References.

Index. Canonical Examples of Weak Asplund Spaces;
Properties of Gâteaux Differentiabilty Spaces and Weak Aspuld Spaces;
Stegall's Class;
Two More Concrete Classes of Banach Spcaes that Lie in Fragmentability; 'Long Sequences' of Linear Projections;
Vacák Spaces and Gul'ko Compacta;
A Characterization of WCG Spaces and of Eberlein Compacta;
Main Open Question and Problems.

Marián J. Fabian is the author of Gateaux Differentiability of Convex Functions and Topology: Weak Asplund Spaces, published by Wiley.