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Isometries in Banach Spaces
Vector-valued Function Spaces and Operator Spaces, Volume Two
By: James E. Jamison, Richard J. Fleming
Hardcover | 15 November 2007 | Edition Number 1
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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.
Industry Reviews
"This is a well-written, highly self-contained book which presents the results and their proofs in an accessible way. The results are complemented with an interesting Notes and Remarks section at the end of each chapter which points the interested reader to paths for further investigation. An extensive bibliography is provided. The two volumes provide not only a very good introduction to the subject but also a nice reference tool for experts."
-Miguel Martin, Mathematical Reviews, Issue 2009i
Praise for Volume One:"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
ISBN: 9781584883869
ISBN-10: 1584883863
Series: Monographs and Surveys in Pure and Applied Mathematics : Book 2
Published: 15th November 2007
Format: Hardcover
Language: English
Number of Pages: 244
Audience: Professional and Scholarly
Publisher: Taylor & Francis Inc
Country of Publication: GB
Edition Number: 1
Dimensions (cm): 23.4 x 15.6 x 2.54
Weight (kg): 0.54
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