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Klappentext This textbook is an introduction to the techniques of summing and nuclear norms. Zusammenfassung This textbook is an introduction to the techniques of summing and nuclear norms. The author's aim is to present a clear and simple account of these ideas and to demonstrate the power of their application to a variety of Banach space questions. The style is expository and the only prerequisite is a beginner's course on Wormed linear spaces and a minimal knowledge of functional analysis. Inhaltsverzeichnis 0. Banach space background; 1. Finite rank operators: trace and 1-nuclear norm; 2. Finite sequences of elements : the quantities ? ? 3. The summing norms; 4. Other nuclear norms: duality with the summing norms; 5. Pietsch's theorem and its applications; 6. Averaging: type 2 and cotype 2 constants; 7. More averaging: Khinchin's inequality and related results; 8. Integral methods: Gaussian averaging; 9. 2-dominated spaces; 10. Grothendieck's inequality; 11. The interpolation method for Grothendieck-type theorems; 12. Results connected with the basis constant; 13. Estimation of summing norms using a restricted number of elements; 14. Pisier's theorem for pi2,1; 15. Tensor products of operators; 16. Trace duality revisited: integral norms; 17. Applications of local reflexivity; 18. Cone-summing norms.
