Isometrics on Banach Spaces

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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

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Table of Contents

Banach's Characterization of Isometries on C(Q)
The Mazur-Ulam Theorem
The Wold Decomposition
Notes and Remarks
Eilenberg's Theorem
The Nonsurjective case
A Theorem of Vesentini
Notes and Remarks
Lamperti's Results
Subspaces of L(p) and the Extension Theorem
Bochner Kernels
Notes and Remarks
Isometries of the Hardy Spaces of the disk
Bergman spaces
Bloch Spaces
S(p) Spaces
Notes and Remarks
Lumer's Method for Orlicz Spaces
Zaidenberg's Generalization
Musielak-Orlicz Spaces
Notes and Remarks
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

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