Entropy, Compactness and the Approximation of Operators (Cambridge Tracts in Mathematics)

Carl, Bernd/ Stephani, Irmtraud

Cambridge University Press（2008/11発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 288 p.
• 言語 ENG
• 商品コード 9780521090940
• DDC分類 515.7

Full Description

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.

Contents

1. Entropy quantities; 2. Approximation quantities; 3. Inequalities of Bernstein-Jackson type; 3. Inequalities of Berstein-Jackson type; 4. A refined Riesz theory; 5. Operators with values in C(X); 6. Operator theoretical methods in the local theory of Banach spaces.