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Geometry and probability in Banach spaces

Author: Laurent Schwartz; Paul R Chernoff
Publisher: Berlin ; New York : Springer-Verlag, 1981.
Series: Lecture notes in mathematics (Springer-Verlag), 852.
Edition/Format:   Print book : EnglishView all editions and formats
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Additional Physical Format: Online version:
Schwartz, Laurent.
Geometry and probability in Banach spaces.
Berlin ; New York : Springer-Verlag, 1981
(OCoLC)654325781
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Laurent Schwartz; Paul R Chernoff
ISBN: 038710691X 9780387106915 354010691X 9783540106913
OCLC Number: 7462049
Description: x, 101 pages : illustrations ; 25 cm.
Contents: 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).
Series Title: Lecture notes in mathematics (Springer-Verlag), 852.
Responsibility: Laurent Schwartz ; notes by Paul R. Chernoff.

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