Volume of Convex Bodies and Banach Space Geometry

Klappentext A self-contained presentation of results relating the volume of convex bodies and Banach space geometry. Zusammenfassung 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.

Dettagli sul prodotto

• Autori: Gilles Pisier, Gilles (Universite De Paris VI (Pierre Et Pisier, Gilles (Universite de Paris VI (Pierre et Marie Curie)) Pisier, Gillies Pisier
• Con la collaborazione di: Bela Bollobas (Editore), W. Fulton (Editore)
• Editore: Cambridge University Press ELT
• Lingue: Inglese
• Formato: Tascabile
• Pubblicazione: 27.05.1999
• EAN: 9780521666350
• ISBN: 978-0-521-66635-0
• Pagine: 268
• Serie: Cambridge Tracts in Mathematics; Cambridge Tracts in Mathematic
• Categoria: Scienze naturali, medicina, informatica, tecnica > Matematica > Geometria