Gilles PisierThe Volume of Convex Bodies and Banach Space Geometry
Herausgeber: Bollobas, Bela; Fulton, W.
Gilles PisierThe Volume of Convex Bodies and Banach Space Geometry
Herausgeber: Bollobas, Bela; Fulton, W.
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A self-contained presentation of results relating the volume of convex bodies and Banach space geometry.
Introduction
1. Notation and preliminary background
2. Gaussian variables. K-convexity
3. Ellipsoids
4. Dvoretzky's theorem
5. Entropy, approximation numbers, and Gaussian processes
6. Volume ratio
7. Milman's ellipsoids
8. Another proof of the QS theorem
9. Volume numbers
10. Weak cotype 2
11. Weak type 2
12. Weak Hilbert spaces
13. Some examples: the Tsirelson spaces
14. Reflexivity of weak Hilbert spaces
15. Fredholm determinants
Final remarks
Bibliography
Index.
