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Isometrics on Banach Spaces
     

Isometrics on Banach Spaces

by Richard J. Fleming, James E. Jamison
 

ISBN-10: 1584880406

ISBN-13: 9781584880400

Pub. Date: 12/23/2002

Publisher: Taylor & Francis

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 classical function spaces. Designed for both experts and beginners in the field, their treatment presents a history of the subject, the important results, and a look at some of the wide

Overview

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 classical function spaces. Designed for both experts and beginners in the field, their treatment presents 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. Focuses on isometries on function spaces Presents the material according to the different classes of Banach spaces Offers self-contained chapters that allow readers to go immediately to any particular point of interest Includes an extensive bibliography

Product Details

ISBN-13:
9781584880400
Publisher:
Taylor & Francis
Publication date:
12/23/2002
Series:
Monographs and Surveys in Pure and Applied Mathematics Series , #129
Pages:
208
Product dimensions:
6.40(w) x 9.50(h) x 0.64(d)

Table of Contents

BEGINNINGS
Introduction
Banach's Characterization of Isometries on C(Q)
The Mazur-Ulam Theorem
Orthogonality
The Wold Decomposition
Notes and Remarks
CONTINUOUS FUNCTION SPACES—THE BANACK-STONE THEOREM
Introduction
Eilenberg's Theorem
The Nonsurjective case
A Theorem of Vesentini
Notes and Remarks
THE L(p) SPACES
Introduction
Lamperti's Results
Subspaces of L(p) and the Extension Theorem
Bochner Kernels
Notes and Remarks
ISOMETRIES OF SPACES OF ANALYTIC FUNCTIONS
Introduction
Isometries of the Hardy Spaces of the disk
Bergman spaces
Bloch Spaces
S(p) Spaces
Notes and Remarks
REARRANGEMENT INVARIANT SPACES
Introduction
Lumer's Method for Orlicz Spaces
Zaidenberg's Generalization
Musielak-Orlicz Spaces
Notes and Remarks
BANACH ALGEBRAS
Introduction
Kadison's Theorem
Subdifferentiability and Kadison's Theorem
The Nonsurjective Case of Kadison's theorem
The Algebras C(1) and AC
Douglas Algebras
Notes and Remarks
BIBLIOGRAPHY
INDEX

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