Journal of Inequalities and Applications
Volume 6 (2000), Issue 2, Pages 119-147

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

Copyright © 2000 Bernd Carl and David E. Edmunds. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.