Journal of Inequalities and Applications 
Volume 6 (2000), Issue 2, Pages 119-147
doi:10.1155/S102558340100008X

Entropy of C(X)-valued operators and diverse applications

Bernd Carl1 and David E. Edmunds2

 1Mathematisches Institut, Friedrich-Schiller-Universität Jena, Jena D-07740, Germany
2School of Mathematical Sciences, University of Sussex, Brighton BN1 9QH, UK
Received 12 October 1999; Revised 20 October 1999

Abstract

We investigate how the metric entropy of C(X)-valued operators influences the entropy behaviour of special operators, such as integral or matrix operators. Various applications are given, to the eigenvalue distributions of operators and to the metric entropy of convex hulls of precompact sets in Banach spaces, for example. In particular, we provide metric entropy conditions on operators sufficient to ensure that the operators are in certain Schatten classes.