Geometry and Probability in Banach Spaces

1. Auflage 1981
ISBN: 978-3-540-10691-3
Verlag: Springer

Buch, Englisch, Band 852, 108 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 195 g

Reihe: Lecture Notes in Mathematics

Springer Book Archives

Zielgruppe

Research

Autoren/Hrsg.

Schwartz, L.

Weitere Mitwirkende

Chernoff, P.R.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

Type and cotype for a Banach space p-summing maps.- Pietsch factorization theorem.- Completely summing maps. Hilbert-Schmidt and nuclear maps.- p-integral maps.- Completely summing maps: Six equivalent properties. p-Radonifying maps.- Radonification Theorem.- p-Gauss laws.- Proof of the Pietsch conjecture.- p-Pietsch spaces. Application: Brownian motion.- More on cylindrical measures and stochastic processes.- Kahane inequality. The case of Lp. Z-type.- Kahane contraction principle. p-Gauss type the Gauss type interval is open.- q-factorization, Maurey's theorem Grothendieck factorization theorem.- Equivalent properties, summing vs. factorization.- Non-existence of (2+?)-Pietsch spaces, Ultrapowers.- The Pietsch interval. The weakest non-trivial superproperty. Cotypes, Rademacher vs. Gauss.- Gauss-summing maps. Completion of grothendieck factorization theorem. TLC and ILL.- Super-reflexive spaces. Modulus of convexity, q-convexity "trees" and Kelly-Chatteryji Theorem Enflo theorem. Modulus of smoothness, p-smoothness. Properties equivalent to super-reflexivity.- Martingale type and cotype. Results of Pisier. Twelve properties equivalent to super-reflexivity. Type for subspaces of Lp (Rosenthal Theorem).