-measures in Minkowski planes.
Ideal norms and trigonometric orthonormal systems
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.
Ideals induced by Tsirelson submeasures
We use Tsirelson’s Banach space ([2]) to define an P-ideal which refutes a conjecture of Mazur and Kechris (see [12, 9, 8]).
Ideals of extendable and liftable operators.
Se introducen los ideales de operadores que admiten extensión o levantamiento y se presenta una nueva aproximación al estudio de la escisión de sucesiones exactas cortas de espacios de Banach. Se considera la maximalidad de estos ideales y se investiga si son cerrados respecto de los límites puntuales acotados. Se resumen algunos ejemplos y se clarifica el papel de los espacios L1 y L∞.
Ideals of finite rank operators, intersection properties of balls, and the approximation property
We characterize the approximation property of Banach spaces and their dual spaces by the position of finite rank operators in the space of compact operators. In particular, we show that a Banach space E has the approximation property if and only if for all closed subspaces F of , the space ℱ(F,E) of finite rank operators from F to E has the n-intersection property in the corresponding space K(F,E) of compact operators for all n, or equivalently, ℱ(F,E) is an ideal in K(F,E).
Ideals of homogeneous polynomials and weakly compact approximation property in Banach spaces
We show that a Banach space has the weakly compact approximation property if and only if each continuous Banach-valued polynomial on can be uniformly approximated on compact sets by homogeneous polynomials which are members of the ideal of homogeneous polynomials generated by weakly compact linear operators. An analogous result is established also for the compact approximation property.
If E' has the Metric Approximation Property then so Does (E, E').
In a Nonreflexive Space the Subdifferential is Not Onto.
Incomparable, non-isomorphic and minimal Banach spaces
A Banach space contains either a minimal subspace or a continuum of incomparable subspaces. General structure results for analytic equivalence relations are applied in the context of Banach spaces to show that if E₀ does not reduce to isomorphism of the subspaces of a space, in particular, if the subspaces of the space admit a classification up to isomorphism by real numbers, then any subspace with an unconditional basis is isomorphic to its square and hyperplanes, and the unconditional basis has...
Inductive limits of vector-valued sequence spaces.
Let L be a normal Banach sequence space such that every element in L is the limit of its sections and let E = ind En be a separated inductive limit of the locally convex spaces. Then ind L(En) is a topological subspace of L(E).
Inégalité de Brunn-Minkowski-Lusternik, et autres inégalités géométriques et fonctionnelles
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,...
Inégalités isopérimétriques en analyse et probabilités
Inequalities in additive -isometries on linear -normed Banach spaces.
Inequalities of the Kahane-Khinchin type and sections of -balls
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 , p > -2.
Infinite asymptotic games
We study infinite asymptotic games in Banach spaces with a finite-dimensional decomposition (F.D.D.) and prove that analytic games are determined by characterising precisely the conditions for the players to have winning strategies. These results are applied to characterise spaces embeddable into sums of finite dimensional spaces, extending results of Odell and Schlumprecht, and to study various notions of homogeneity of bases and Banach spaces. The results are related to questions of rapidity...
Infinite Asymptotic Games and (*)-Embeddings of Banach Spaces
We use methods of infinite asymptotic games to characterize subspaces of Banach spaces with a finite-dimensional decomposition (FDD) and prove new theorems on operators. We consider a separable Banach space X, a set of sequences of finite subsets of X and the -game. We prove that if satisfies some specific stability conditions, then Player I has a winning strategy in the -game if and only if X has a skipped-blocking decomposition each of whose skipped-blockings belongs to . This result implies that...
Infinite Dimensional Polytopes.
Infinite-dimensional sets of constant width and their applications.
Sets of constant width appear as a curiosity in the context of finite-dimensional Euclidean spaces. These sets are convex bodies of such an space with the property that the distance between any two distinct parallel supporting hyperplanes is constant. The easiest example of a set of constant width which is not a ball is the so called Reuleaux triangle in the Euclidean plane. This is the intersection of three closed discs of radius r, whose centers are the vertices of an equilateral triangle of side...
Infinitely divisible probability measures and the converse Kolmogorov inequality in Banach spaces
Inner M-ideals in Banach algebras.