Isometries in Banach Spaces: Vector-valued Function Spaces and Operator Spaces, Volume Two (Monographs and Surveys in Pure and Applied Mathematics) - Hardcover

Fleming, Richard J.; Jamison, James E.

Hardcover

ISBN 10: 1584883863 ISBN 13: 9781584883869

Publisher: Chapman and Hall/CRC, 2007

Synopsis

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.

About this title

About the Author

Richard J. Fleming, James E. Jamison

Edition details

• Publisher: Chapman and Hall/CRC
• Publication date: 2007
• Language: English
• ISBN 10: 1584883863
• ISBN 13: 9781584883869
• Binding: Hardcover
• Edition number: 1
• Number of pages: 244