Summing and Nuclear Norms in Banach Space Theory (Paperback)

0. Banach space background; 1. Finite rank operators: trace and 1-nuclear norm; 2. Finite sequences of elements : the quantities μ1, μ2; 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.