Geometry and probability in Banach spaces
著者
書誌事項
Geometry and probability in Banach spaces
（Lecture notes in mathematics, 852）
Springer-Verlag, 1981
- : Berlin
- : New York
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注記
Bibliography: p. 99
Includes index
内容説明・目次
目次
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).
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