Isometries in Banach Spaces: Vector-valued Function Spaces and Operator Spaces, Volume Two

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ISBN: 9781584883869 | 1584883863
Cover: Hardcover
Copyright: 11/15/2007

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A continuation of the authors' previous book, Isometries on Banach Spaces: Vector-valued Function Spaces, Volume Two covers much of the work that has been done on characterizing isometries on various Banach spaces.

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Preface	p. vii
The Banach-Stone Property	p. 1
Introduction	p. 1
Strictly Convex Spaces and Jerison's Theorem	p. 3
M Summands and Cambern's Theorem	p. 10
Centralizers, Function Modules, and Behrends' Theorem	p. 18
The Nonsurjective Vector-Valued Case	p. 28
The Nonsurjective Case for Nice Operators	p. 36
Notes and Remarks	p. 46
The Banach-Stone Property for Bochner Spaces	p. 51
Introduction	p. 51
L[superscript p] Functions with Values in Hilbert Space	p. 53
L[superscript p] Functions with Values in Banach Space	p. 63
L[superscript 2] Functions with Values in a Banach Space	p. 72
Notes and Remarks	p. 77
Orthogonal Decompositions	p. 83
Introduction	p. 83
Sequence Space Decompositions	p. 84
Hermitian Elements and Orthonormal Systems	p. 97
The Case for Real Scalars: Functional Hilbertian Sums	p. 105
Decompositions with Banach Space Factors	p. 115
Notes and Remarks	p. 128
Matrix Spaces	p. 137
Introduction	p. 137
Morita's Proof of Schur's Theorem	p. 138
Isometries for (p, k) Norms on Square Matrix Spaces	p. 140
Isometries for (p, k) Norms on Rectangular Matrix Spaces	p. 147
Notes and Remarks	p. 155
Isometries of Norm Ideals of Operators	p. 159
Introduction	p. 159
Isometries of C[subscript p]	p. 160
Isometries of Symmetric Norm Ideals: Sourour's Theorem	p. 166
Noncommutative L[superscript p] Spaces	p. 172
Notes and Remarks	p. 179
Minimal and Maximal Norms	p. 183
Introduction	p. 183
An Infinite-Dimensional Space with Trivial Isometries	p. 184
Minimal Norms	p. 186
Maximal Norms and Forms of Transitivity	p. 190
Notes and Remarks	p. 196
Epilogue	p. 201
Reflexivity of the Isometry Group	p. 201
Adjoint Abelian Operators	p. 204
Almost Isometries	p. 207
Distance One Preserving Maps	p. 210
Spectral Isometries	p. 210
Isometric Equivalence	p. 211
Potpourri	p. 212
Bibliography	p. 213
Index	p. 229
Table of Contents provided by Ingram. All Rights Reserved.

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Isometries in Banach Spaces: Vector-valued Function Spaces and Operator Spaces, Volume Two

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