Absolutely Summing Operators
Published on 12. June 2008
Book
Paperback/Softback
492 pages
978-0-521-06493-4 (ISBN)
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 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.
Reviews / Votes
"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 ReviewsMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Product notice
Paperback (trade)
Illustrations
Worked examples or Exercises
Dimensions
Height: 229 mm
Width: 152 mm
Thickness: 29 mm
Weight
792 gr
ISBN-13
978-0-521-06493-4 (9780521064934)
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Schweitzer Classification
Persons
Content
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.