Fleming / Jamison Isometries in Banach Spaces

Vector-valued Function Spaces and Operator Spaces, Volume Two
Erscheinungsjahr 2007
ISBN: 978-1-4200-1020-6
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 248 Seiten

Reihe: Monographs and Surveys in Pure and Applied Mathematics

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.

Zielgruppe

Graduate students and researchers in functional analysis and operator theory.

Autoren/Hrsg.

Fleming, Richard J.

Jamison, James E.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis

Inhaltsverzeichnis

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

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