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Tensor norms and operator ideals

Author: Andreas Defant; Klaus Floret
Publisher: Amsterdam ; New York : North-Holland, 1993.
Series: North-Holland mathematics studies, 176.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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 ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Defant, Andreas.
Tensor norms and operator ideals.
Amsterdam ; New York : North-Holland, 1993
(DLC) 92036408
(OCoLC)26810071
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Andreas Defant; Klaus Floret
ISBN: 9780444890917 0444890912 9780080872872 0080872875 1281789674 9781281789679
OCLC Number: 316570365
Description: 1 online resource (xi, 566 pages) : illustrations.
Contents: Basic Concepts. Bilinear Mappings. The Algebraic Theory of Tensor Products. The Projective Norm. The Injective Norm. The Approximation Property. Duality of the Projective and Injective Norm. The Natural Norm on the p-Integrable Functions. Absolutely and Weakly p-Summable Series and Averaging Techniques. Operator Ideals. Integral Operators. Absolutely p-Summing Operators.Tensor Norms. Definition and Examples. The Five Basic Lemmas. Grothendieck's Inequality. Dual Tensor Norms. The Bounded Approximation Property. The Representation Theorem for Maximal Operator Ideals. (p-q)-Factorable Operators. (p-q)-Dominated Operators. Projective and Injective Tensor Norms. Accessible Tensor Norms and Operator Ideals. Minimal Operator Ideals. Lgp-Spaces. Stable Measures. Composition of Accessible Operator Ideals. More About Lp and Hilbert Spaces. Grothendieck's Fourteen Natural Norms.Special Topics. More Tensor Norms. The Calculus of Traced Tensor Norms. The Vector Valued Fourier Transform. Pisier's Factorization Theorem. Mixing Operators. The Radon-Nikodym Property for Tensor Norms and Reflexivity. Tensorstable Operator Ideals. Tensor Norm Techniques for Locally Convex Spaces.Appendices. References. Index.
Series Title: North-Holland mathematics studies, 176.
Responsibility: Andreas Defant, Klaus Floret.
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Abstract:

Shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. This work presents the theory of tensor norms as designed by Grothendieck  Read more...

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