TY  - BOOK
AU  - Schwartz,Laurent
AU  - Chernoff,Paul R.
ED  - SpringerLink (Online service)
TI  - Geometry and Probability in Banach Spaces
T2  - Lecture Notes in Mathematics,
SN  - 9783540386179
AV  - QA273.A1-274.9 
U1  - 519.2 23
PY  - 1981///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Geometry
KW  - Distribution (Probability theory)
KW  - Probability Theory and Stochastic Processes
N1  - 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)
UR  - http://dx.doi.org/10.1007/BFb0096723
ER  -