Geometry and Probability in Banach Spaces

✍ Scribed by Laurent Schwartz, Paul R. Chernoff (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1981
• Tongue: English
• Leaves: 123
• Series: Lecture Notes in Mathematics 852
• Edition: 1
• Category: Library

✦ 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

✦ Subjects

Probability Theory and Stochastic Processes; Geometry