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Isometries in Banach Spaces

Vector-valued Function Spaces and Operator Spaces, Volume Two

Isometries in Banach Spaces by Richard J. Fleming
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Preface
THE BANACHSTONE PROPERTY
Introduction
Strictly Convex Spaces and Jerison’s Theorem
M Summands and Cambern’s Theorem
Centralizers, Function Modules, and Behrend’s Theorem
The Nonsurjective Vector-Valued Case
The Nonsurjective Case for Nice Operators
Notes and Remarks
The Banach–Stone Property for Bochner Spaces
Introduction
LP Functions with Values in Hilbert Space
LP Functions with Values in Banach Space
L2 Functions with Values in Banach Space
Notes and Remarks
Orthogonal Decompostions
Introduction
Sequence Space Decompositions
Hermitian Elements and Orthonormal Systems
The Case for Real Scalars: Functional Hilbertian Sums
Decompositions with Banach Space Factors
Notes and Remarks
Matrix Spaces
Introduction
Morita’s Proof of Schur’s Theorem
Isometries for (p, k) Norms on Square Matrix Spaces
Isometries for (p, k) Norms on Rectangular Matrix Spaces
Notes and Remarks
Isometries of Norm Ideals of Operators
Introduction
Isometries of CP
Isometries of Symmetric Norm Ideals: Sourour’s Theorem
Noncommutative LP Spaces
Notes and Remarks
Minimal and Maximal Norms
Introduction
An Infinite-Dimensional Space with Trivial Isometries
Minimal Norms
Maximal Norms and Forms of Transitivity
Notes and Remarks
Epilogue
Reflexivity of the Isometry Group
Adjoint Abelian Operators
Almost Isometries
Distance One Preserving Maps
Spectral Isometries
Isometric Equivalence
Potpourri
BIBLIOGRAPHY
INDEX
CRC Press; November 2007
245 pages; ISBN 9781420010206
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Title: Isometries in Banach Spaces
Author: Richard J. Fleming; James E. Jamison
 
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