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＜E-Book＞
Geometry and Probability in Banach Spaces / by L. Schwartz
(Lecture Notes in Mathematics. ISSN:16179692 ; 852)

Edition	1st ed. 1981.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	1981
Size	XII, 108 p : online resource
Authors	*Schwartz, L author SpringerLink (Online service)
Subjects	LCSH:Probabilities LCSH:Geometry FREE:Probability Theory FREE:Geometry
Notes	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) HTTP:URL=https://doi.org/10.1007/BFb0096723

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