Vector-valued function spaces
著者
書誌事項
Vector-valued function spaces
（Chapman & Hall/CRC monographs and surveys in pure and applied mathematics, 138 . Isometries on Banach spaces ; v. 2）
Chapman & Hall/CRC, c2008
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注記
Includes bibliographical references (p. 213-227) and index
内容説明・目次
内容説明
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 C0(Q, X) to C0(K, Y) so that the property involves pairs (X, Y) of spaces. The next chapter examines spaces X for which the isometries on LP( , 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.
目次
Preface. The Banach-Stone Property. The Banach-Stone Property for Bochner Spaces. Orthogonal Decompostions. Matrix Spaces. Isometries of Norm Ideals of Operators. Minimal and Maximal Norms. Epilogue. Bibliography. Index.
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