Absolutely Summing Operators

This text provides the beginning graduate student with an account of p-summing and related operators.

Joe Diestel (Author), Hans Jarchow (Author), Andrew Tonge (Author)

9780521431682, Cambridge University Press

Hardback, published 27 April 1995

492 pages
23.5 x 15.7 x 3 cm, 0.8 kg

"...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

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 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 non-trivial applications to, for example, harmonic analysis, probability and measure theory, and operator theory. Graduate students and researchers from real, complex and functional analysis, and probability theory will benefit from this account.

Introduction
1. Unconditioned and absolute summability in Banach spaces
2. Fundamentals of p-summing operators
3. Summing operators on Cp-spaces
4. Operators on Hilbert spaces and summing operators
5. p-Integral operators
6. Trace duality
7. 2-Factorable operators
8. Ultraproducts and local reflexivity
9. p-Factorable operators
10. (q, p)-Summing operators
11. Type and cotype: the basics
12. Randomised series and almost summing operators
13. K-Convexity and B-convexity
14. Spaces with finite cotype
15. Weakly compact operators on C(K)-spaces
16. Type and cotype in Banach lattices
17. Local unconditionality
18. Summing algebras
19. Dvoretzky's theorem and factorization of operators
References
Indexes.

Subject Areas: Calculus & mathematical analysis [PBK]