This book gives a self-contained presentation of some recent results, relating the volume of convex bodies in n-dimensional Euclidean space and the geometry of the corresponding finite-dimensional normed spaces. This employs classical ideas from the theory of convex sets, probability theory, approximation theory and the local theory of Banach spaces.
Inhaltsverzeichnis
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.
Klappentext
A self-contained presentation of results relating the volume of convex bodies and Banach space geometry.
