Tensor norms and operator ideals /

The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator id...

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Bibliographic Details
Main Author:	Defant, Andreas
Corporate Author:	ScienceDirect (Online service)
Other Authors:	Floret, Klaus
Format:	eBook
Language:	English
Language Notes:	English.
Published:	Amsterdam ; New York : North-Holland, 1993.
Series:	North-Holland mathematics studies ; 176.
Subjects:	Tensor products. Operator ideals. Produits tensoriels. Idéaux d'opérateurs. MATHEMATICS > Vector Analysis. Operator ideals Tensor products Tensoren. Operatoren. Tensor analysis Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

Front Cover; Tensor Norms and Operator Ideals; Copyright Page; Contents; Introduction; Chapter I: Basic Concepts; 1. Bilinear Mappings; 2. The Algebraic Theory of Tensor Products; 3. The Projective Norm; 4. The Injective Norm; 5. The Approximation Property; 6. Duality of the Projective and Injective Norm; 7. The Natural Norm on the p-Integrable Functions; 8. Absolutely and Weakly p-Summable Series and Averaging Techniques; 9. Operator Ideals; 10. Integral Operators; 11. Absolutely p-Summing Operators; Chapter II: Tensor Norms.; 12. Definition and Examples; 13. The Five Basic Lemmas
14. Grothendieck's Inequality15. Dual Tensor Norms; 16. The Bounded Approximation Property; 17. The Representation Theorem for Maximal Operator Ideals; 18. (p, q)-Factorable Operators; 19. (p, q)-Dominated Operators; 20. Projective and Injective Tensor Norms; 21. Accessible Tensor Norms and Operator Ideals; 22. Minimal Operator Ideals; 23. Lgp-Spaces; 24. Stable Measures; 25. Composition of Accessible Operator Ideals; 26. More About Lp and Hilbert Spaces; 27. Grothendieck's Fourteen Natural Norms; Chapter III: Special Topics; 28. More Tensor Norms; 29. The Calculus of Traced Tensor Norms
30. The Vector Valued Fourier Transform31. Pisier's Factorization Theorem; 32. Mixing Operators; 33. The Radon-Nikodým Property for Tensor Norms and Reflexivity; 34. Tensorstable Operator Ideals; 35. Tensor Norm Techniques for Locally Convex Spaces; Appendices:; A. Some Structural Properties of Banach Spaces; B. Integration Theory; C. Representable Operators; D. The Radon-Nikodým Property; Bibliography; List of Symbols; Index