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Entropy of -valued operators and diverse applications

Keywords: Entropy , Integral operators , Schatten classes

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Abstract:

We investigate how the metric entropy of -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.

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