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.

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.