Isometries in Banach Spaces
Vector-valued Function Spaces and Operator Spaces, Volume Two
Seiten
2007
Chapman & Hall/CRC (Verlag)
978-1-58488-386-9 (ISBN)
Chapman & Hall/CRC (Verlag)
978-1-58488-386-9 (ISBN)
Focuses on canonical-form characterizations of isometries on Banach spaces. This monograph explores the topic in the context of vector-valued function spaces and operator spaces. It looks at some of the wide variety of methods used in addressing the characterization problem in various types of spaces.
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(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.
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(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.
Richard J. Fleming, James E. Jamison
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.
| Erscheint lt. Verlag | 11.12.2007 |
|---|---|
| Reihe/Serie | Monographs and Surveys in Pure and Applied Mathematics |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 544 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-58488-386-3 / 1584883863 |
| ISBN-13 | 978-1-58488-386-9 / 9781584883869 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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