Entropy, Compactness and the Approximation of Operators

Bernd Carl, Irmtraud Stephani

• Publisher: Cambridge University Press
• Year: 2008
• Print ISBN: 9780521090940
• eBook ISBN: 9780511982033
• Topic: Mathematics
• Subtopic: Abstract Algebra
• Index: Mathematics

Entropy quantities are connected with the 'degree of compactness' of compact or precompact spaces, and so are appropriate tools for investigating linear and compact operators between Banach spaces. The main intention of this Tract is to study the relations between compactness and other analytical properties, e.g. approximability and eigenvalue sequences, of such operators. The authors present many generalized results, some of which have not appeared in the literature before. In the final chapter, the authors demonstrate that, to a certain extent, the geometry of Banach spaces can also be developed on the basis of operator theory. All mathematicians working in functional analysis and operator theory will welcome this work as a reference or for advanced graduate courses.

Table of contents

• Cover
• Frontmatter
• Contents
• Preface
• Introduction
• Entropy quantities
• Approximation quantities
• Inequalities of Bernstein–Jackson type
• A refined Riesz theory
• Operators with values in C(X)
• Operator theoretical methods in the local theory of Banach spaces
• References
• List of symbols
• Index