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

ISBN-13: 9781584883869 / Angielski / Twarda / 2007 / 248 str.

Richard J. Fleming; Fleming J. Fleming; James E. Jamison

Opis

The interest of these authors lies in explicit, canonical-form characterizations of isometries on Banach spaces, and in this monograph, they explore the topic in the context of vector-valued function spaces a nd operator spaces. Designed for both experts and beginners in the field, their treatment outlines a history of the subject, the important results, and a look at some of the wide variety of methods used in addressing the characterization problem in various types of spaces. The authors faithfully report the results of other researchers' original papers and offer some enlightening clarifications. Each chapter is self-contained and includes notes and remarks that touch upon related results and other approaches not addressed in the main text.

Spis treści

Preface
THE BANACH–STONE 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
L^P Functions with Values in Hilbert Space
L^P 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 C_P
Isometries of Symmetric Norm Ideals: Sourour’s Theorem
Noncommutative L^P 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

O autorze

Richard J. Fleming, James E. Jamison