Overview

A continuation of the authors previous book, Isometries on Banach Spaces: Vector-valued Function Spaces and Operator Spaces, Volume Two covers much of the work that has been done on characterizing isometries on various Banach spaces. Picking up where the first volume left off, the book begins with a chapter on the Banach Stone property. The authors consider the case where the isometry is from C 0( Q, X ) to C 0( K, Y ) so that the property involves pairs ( X, Y ) of spaces. The next chapter examines spaces X for which the isometries on LP ( μ, X ) can be described as a generalization of the form given by Lamperti in the scalar case. The book then studies isometries on direct sums of Banach and Hilbert spaces, isometries on spaces of matrices with a variety of norms, and isometries on Schatten classes. It subsequently highlights spaces on which the group of isometries is maximal or minimal. The final chapter addresses more peripheral topics, such as adjoint abelian operators and spectral isometries. Essentially self-contained, this reference explores a fundamental aspect of Banach space theory. Suitable for both experts and newcomers to the field, it offers many references to provide solid coverage of the literature on isometries.

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9781322626840

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About volume one, Isometries on Banach Spaces: Function Spaces: This is a very well written book. The authors have done a remarkable job in collecting this material and in exposing it in a very clear style. It will be an important reference tool for analysts, experts and nonexperts, and it will provide a clear and direct path to several topics of current research interest. - Juan J. Font, Mathematical Reviews, Issue 2004j

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