Isometries on Banach Spaces : function spaces

Richard J. Fleming

ISBN 10: 1584880406 / ISBN 13: 9781584880400

Published by Taylor & Francis Inc Dez 2002, 2002

About this Item

Neuware - Surveys investigations of Banach-space isometries. This volume emphasizes the characterization of isometries and focuses on establishing the type of explicit, canonical form in a variety of settings. It describes the isometries on classical function spaces. It explores isometries on Banach algebras.

Seller Inventory # 9781584880400

Bibliographic Details

• Title: Isometries on Banach Spaces : function spaces
• Publisher: Taylor & Francis Inc Dez 2002
• Publication Date: 2002
• Language: English
• ISBN 10: 1584880406
• ISBN 13: 9781584880400
• Binding: Buch
• Condition: Neu
• Dimensions: 234W x 156H x 0D millimeters 234 millimeters width by 156 millimeters height by 0 millimeters depth
• Weight: 445 grams

About this title

Synopsis

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.

About the Author

Fleming, Richard J.; Jamison, James E.