Schwartz, Laurent.
Geometry and Probability in Banach Spaces [electronic resource] / by Laurent Schwartz, Paul R. Chernoff. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1981. - XII, 108 p. online resource. - Lecture Notes in Mathematics, 852 0075-8434 ; . - Lecture Notes in Mathematics, 852 .
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).
9783540386179
10.1007/BFb0096723 doi
Mathematics.
Geometry.
Distribution (Probability theory).
Mathematics.
Probability Theory and Stochastic Processes.
Geometry.
QA273.A1-274.9 QA274-274.9
519.2
Geometry and Probability in Banach Spaces [electronic resource] / by Laurent Schwartz, Paul R. Chernoff. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1981. - XII, 108 p. online resource. - Lecture Notes in Mathematics, 852 0075-8434 ; . - Lecture Notes in Mathematics, 852 .
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).
9783540386179
10.1007/BFb0096723 doi
Mathematics.
Geometry.
Distribution (Probability theory).
Mathematics.
Probability Theory and Stochastic Processes.
Geometry.
QA273.A1-274.9 QA274-274.9
519.2