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Absolutely Summing Operators : Cambridge Studies in Advanced Mathematics - Joe Diestel

Absolutely Summing Operators

Cambridge Studies in Advanced Mathematics

Hardcover Published: 27th April 1995
ISBN: 9780521431682
Number Of Pages: 492

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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.

Industry Reviews

"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

Unconditional and Absolute Summability in Banach Spacesp. 1
Fundamentals of p-Summing Operatorsp. 31
Summing Operators on L[subscript p]-Spacesp. 60
Operators on Hilbert Spaces and Summing Operatorsp. 76
p-Integral Operatorsp. 95
Trace Dualityp. 125
2-Factorable Operatorsp. 154
Ultraproducts and Local Reflexivityp. 169
p-Factorable Operatorsp. 185
(q,p)-Summing Operatorsp. 197
Type and Cotype: The Basicsp. 211
Randomized Series and Almost Summing Operatorsp. 230
K-Convexity and B-Convexityp. 258
Spaces with Finite Cotypep. 283
Weakly Compact Operators on C(K)-Spacesp. 309
Type and Cotype in Banach Latticesp. 326
Local Unconditionalityp. 344
Summing Algebrasp. 373
Dvoretzky's Theorem and Factorization of Operatorsp. 396
Referencesp. 435
Author Indexp. 465
Subject Indexp. 469
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780521431682
ISBN-10: 0521431689
Series: Cambridge Studies in Advanced Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 492
Published: 27th April 1995
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 3.2
Weight (kg): 0.79