Tensor Norms and Operator Ideals

Abstract

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.