Geometry and Probability in Banach Spaces

Laurent Schwartz, Paul R. Chernoff (auth.)9780387106915, 0-387-10691-X

Table of contents :
Type and cotype for a Banach space p-summing maps….Pages 1-5
Pietsch factorization theorem….Pages 5-9
Completely summing maps. Hilbert-Schmidt and nuclear maps….Pages 9-15
p-integral maps….Pages 15-17
Completely summing maps: Six equivalent properties. p-Radonifying maps….Pages 18-25
Radonification Theorem….Pages 25-29
p-Gauss laws….Pages 29-32
Proof of the Pietsch conjecture….Pages 32-38
p-Pietsch spaces. Application: Brownian motion….Pages 38-41
More on cylindrical measures and stochastic processes….Pages 42-45
Kahane inequality. The case of L p . Z-type….Pages 46-51
Kahane contraction principle. p-Gauss type the Gauss type interval is open….Pages 51-55
q-factorization, Maurey’s theorem Grothendieck factorization theorem….Pages 56-61
Equivalent properties, summing vs. factorization….Pages 61-67
Non-existence of (2+ɛ)-Pietsch spaces, Ultrapowers….Pages 67-72
The Pietsch interval. The weakest non-trivial superproperty. Cotypes, Rademacher vs. Gauss….Pages 72-78
Gauss-summing maps. Completion of grothendieck factorization theorem. TLC and ILL….Pages 78-85
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….Pages 85-92
Martingale type and cotype. Results of Pisier. Twelve properties equivalent to super-reflexivity. Type for subspaces of L p (Rosenthal Theorem)….Pages 92-98