Isometries on Banach Spaces: function spaces / Edition 1

by Richard J. Fleming, James E. Jamison

Overview

Fundamental to the study of any mathematical structure is an understanding of its symmetries. In the class of Banach spaces, this leads naturally to a study of isometries-the linear transformations that preserve distances. In his foundational treatise, Banach showed that every linear isometry on the space of continuous functions on a compact metric space must transform a continuous function x into a continuous function y satisfying y(t) = h(t)x(p(t)), where p is a homeomorphism and |h| is identically one.

Isometries on Banach Spaces: Function Spaces is the first of two planned volumes that survey investigations of Banach-space isometries. This volume emphasizes the characterization of isometries and focuses on establishing the type of explicit, canonical form given above in a variety of settings. After an introductory discussion of isometries in general, four chapters are devoted to describing the isometries on classical function spaces. The final chapter explores isometries on Banach algebras.

This treatment provides a clear account of historically important results, exposes the principal methods of attack, and includes some results that are more recent and some that are lesser known. Unique in its focus, this book will prove useful for experts as well as beginners in the field and for those who simply want to acquaint themselves with this area of Banach space theory.

Product Details

ISBN-13:	9781584880400
Publisher:	Taylor & Francis
Publication date:	12/23/2002
Series:	Monographs and Surveys in Pure and Applied Mathematics , #129
Pages:	208
Product dimensions:	6.12(w) x 9.19(h) x (d)

About the Author

Fleming, Richard J.; Jamison, James E.

Table of Contents

Beginnings. Continuous Function Spaces—The Banach-Stone Theorem. The L(p) Spaces. Isometries of Spaces of Analytic Functions. Rearrangement Invariant Spaces. Banach Algebras. Bibliography. Index.

Editorial Reviews

"This is a very well written book. The authors have done a remarkable job in collecting this material and in exposing it in a very clear style. It will be an important reference tool for analysts, experts and nonexperts, and it will provide a clear and direct path to several topics of current research interest." - Juan J. Font, Mathematical Reviews, Issue 2004j

From the Publisher