Tensor Norms and Operator IdealsBy
- A. Defant, Fachbereich Mathematik, Universität Oldenburg, Oldenburg, Germany
- K. Floret, Fachbereich Mathematik, Universität Oldenburg, Oldenburg, Germany, and IMECC/Unicamp, Campinas/S.P., Brasil
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 Grothendieck in the
Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exercises.
North-Holland Mathematics Studies
Published: November 1992
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.