Absolutely summing operators
著者
書誌事項
Absolutely summing operators
（Cambridge studies in advanced mathematics, 43）
Cambridge University Press, 1995
- : hardback
- : pbk
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注記
"Transferred to digital printing 2005"--T.p. verso of 2005 hardback printing
Bibliography: p. 435-464
Includes indexes
内容説明・目次
内容説明
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.
目次
- 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.
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