Entropy, Compactness and the Approximation of Operators
“Entropy, Compactness and the Approximation of Operators” by Bernd Carl, published by Cambridge University Press on November 27, 2008, is a comprehensive exploration of the connections between entropy quantities and the degree of compactness in compact or precompact spaces. This edition, consisting of 288 pages, delves into the analytical properties of linear and compact operators within Banach spaces, presenting generalized results that contribute to the existing literature.
Readers will find a thorough examination of how compactness relates to approximability and eigenvalue sequences of operators. The text also discusses the potential for developing the geometry of Banach spaces through operator theory. This work serves as a valuable reference for mathematicians engaged in functional analysis and operator theory, as well as for advanced graduate courses in these fields.
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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.
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