Isometries on Banach Spaces

function spaces

Richard J. Fleming, James E. Jamison

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English

Chapman & Hall/CRC
05 September 2019

Mathematics

Series: Monographs and Surveys in Pure and Applied Mathematics

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.

By: Richard J. Fleming, James E. Jamison
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 294g
ISBN: 9780367395575
ISBN 10: 0367395576
Series: Monographs and Surveys in Pure and Applied Mathematics
Pages: 208
Publication Date: 05 September 2019
Audience: College/higher education , General/trade , Primary , ELT Advanced
Format: Paperback
Publisher's Status: Active

Fleming, Richard J.; Jamison, James E.

Reviews for Isometries on Banach Spaces: function spaces

"""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"