Entropy of <inline-formula><graphic file="1029-242X-2001-852528-i1.gif"/></inline-formula>-valued operators and diverse applications

• Main Authors: Edmunds David E, Carl Bernd
• Format: Article
• Language: English
• Published: SpringerOpen 2001-01-01
• Series: Journal of Inequalities and Applications
• Subjects: Entropy; Integral operators; Schatten classes
• Online Access: http://www.journalofinequalitiesandapplications.com/content/6/852528

<p/> <p>We investigate how the metric entropy of <inline-formula><graphic file="1029-242X-2001-852528-i2.gif"/></inline-formula>-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.</p>