Entropy, Compactness and the Approximation of Operators

Erscheinungsjahr 1990
ISBN: 978-0-521-33011-4
Verlag: Cambridge University Press

Buch, Englisch, 287 Seiten, Format (B × H): 152 mm x 228 mm, Gewicht: 538 g

Reihe: Cambridge Tracts in 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.

Autoren/Hrsg.

Carl, Bernd

Stephani, Irmtraud

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

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.