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Ideal norms and trigonometric orthonormal systems

Jörg Wenzel (1994)

Studia Mathematica

We characterize the UMD-property of a Banach space X by sequences of ideal norms associated with trigonometric orthonormal systems. The asymptotic behavior of those numerical parameters can be used to decide whether X is a UMD-space. Moreover, if this is not the case, we obtain a measure that shows how far X is from being a UMD-space. The main result is that all described sequences are not only simultaneously bounded but are also asymptotically equivalent.

Inégalité de Brunn-Minkowski-Lusternik, et autres inégalités géométriques et fonctionnelles

Bernard Maurey (2003/2004)

Séminaire Bourbaki

La théorie des corps convexes a commencé à la fin du xixe siècle avec l’inégalité de Brunn, généralisée ensuite sous la forme de l’inégalité de Brunn-Minkowski-Lusternik, qui s’applique à des ensembles non convexes. Ce thème a depuis longtemps des contacts avec les problèmes isopérimétriques et avec des inégalités d’Analyse telle que les plongements de Sobolev. On développera quelques aspects plus récents des inégalités géométriques, dont certains sont liés à la technique du transport de mesure,...

Inequalities of the Kahane-Khinchin type and sections of $L_{p}$ -balls

A. Koldobsky, A. Pajor, V. Yaskin (2008)

Studia Mathematica

We extend Kahane-Khinchin type inequalities to the case p > -2. As an application we verify the slicing problem for the unit balls of finite-dimensional spaces that embed in $L_{p}$ , p > -2.

Integral mappings and the principle of local reflexivity for noncommutative $L^{1}$ -spaces.

Effros, Edward G., Junge, Marius, Ruan, Zhong-Jin (2000)

Annals of Mathematics. Second Series

Isometric imbeddings of Euclidean spaces into finite dimensional $l_{p}$ -spaces

Hermann König (1995)

Banach Center Publications

It is shown that $l_{2}^{n}$ imbeds isometrically into $l_{4}^{n^{2} + 1}$ provided that n is a prime power plus one, in the complex case. This and similar imbeddings are constructed using elementary techniques from number theory, combinatorics and coding theory. The imbeddings are related to existence of certain cubature formulas in numerical analysis.

Displaying 1 – 5 of 5

Ideal norms and trigonometric orthonormal systems

Inégalité de Brunn-Minkowski-Lusternik, et autres inégalités géométriques et fonctionnelles

Inequalities of the Kahane-Khinchin type and sections of L p -balls

Integral mappings and the principle of local reflexivity for noncommutative L 1 -spaces.

Isometric imbeddings of Euclidean spaces into finite dimensional l p -spaces

Currently displaying 1 – 5 of 5

Inequalities of the Kahane-Khinchin type and sections of $L_{p}$ -balls

Integral mappings and the principle of local reflexivity for noncommutative $L^{1}$ -spaces.

Isometric imbeddings of Euclidean spaces into finite dimensional $l_{p}$ -spaces