Absolutely Summing Operators (Cambridge Studies in Advanced Mathematics, Series Number 43) - Hardcover

Diestel, Joe; Jarchow, Hans; Tonge, Andrew

Hardcover

ISBN 10: 0521431689 ISBN 13: 9780521431682

Publisher: Cambridge University Press, 1995

Synopsis

We can best understand many fundamental processes in analysis by studying and comparing the summability of series in various modes of convergence. This text provides the reader with basic knowledge of real and functional analysis, with an account of p-summing and related operators. The account is panoramic, with detailed expositions of the core results and highly relevant applications to harmonic analysis, probability and measure theory, and operator theory. This is the first time that the subject and its applications have been presented in such complete detail in book form. Graduate students and researchers in real, complex and functional analysis, and probability theory will benefit from this text.

About this title

Book Description:

Many fundamental processes in analysis are best understood by studying and comparing the summability of series in various modes of convergence. This text provides the beginning graduate student, one with basic knowledge real and functional analysis, with an account of p-summing and related operators. The account is panoramic, with detailed expositions of the core results and highly non-trivial applications to, for example,harmonic analysis, probability and measure theory and to operator theory. This is the first time that the subject and its applications have been presented in such complete detail in book form. Graduate students and researchers from real, complex and functional analysis, and probability theory will benefit from perusing this account.

Review:

"Beautifully motivated exposition!" American Mathematical Monthly

"...a very welcome addition to a rather long list of recently published monographs concerning deep mathematics in Banach spaces from the last three decades--it is the first time that the important subject of 'summing operators' has been presented in almost complete detail in book form. Large parts of the book are within reach of graduate students, extensive 'notes and remarks' sections fill even sophisticated corners of the field with light--this book promises to be a future classic....this excellent book will have a wide audience which consists not only of interested students: there will be many mathematicians inside and outside of Banach spcae theory who will use it as a rich source for references and inspiration. Wonderful mathematics presented in striking fashion!" Andreas Defant, Mathematical Reviews

About this edition

• Publisher: Cambridge University Press
• Publication date: 1995
• ISBN 10: 0521431689
• ISBN 13: 9780521431682
• Binding: Hardcover
• Edition number: 1
• Number of pages: 492