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Isometries on Banach Spaces: function spaces (Monographs and Surveys in Pure and Applied Mathematics) - Tapa blanda

Libro 17 de 34: Monographs and Surveys in Pure and Applied Mathematics

Fleming, Richard J.; Jamison, James E.

 
9780367395575: Isometries on Banach Spaces: function spaces (Monographs and Surveys in Pure and Applied Mathematics)
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ISBN 10: 0367395576 ISBN 13: 9780367395575
Editorial: Chapman and Hall/CRC, 2019

Sinopsis

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.

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Acerca del autor

Fleming, Richard J.; Jamison, James E.

De la contraportada

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.

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Editorial
Chapman and Hall/CRC
Año de publicación
2019
Idioma
Inglés
ISBN 10 
0367395576
ISBN 13 
9780367395575
Encuadernación
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Número de edición
1
Número de páginas
208
Contacto del fabricante
Taylor and Francis, GPSR Taylor and Francis
gpsr@taylorandfrancis.com

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München
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Alemania