The weak Radon-Nikodym property in Banach spaces
The -approximation property and the weak topology in tensor products of Banach spaces
The -function in the space .
The -function in -algebras.
Théorème limite central dans les espaces
Théorèmes de factorisation dans les espaces
Théorèmes de factorisation dans les espaces (suite)
Theorems of Krein Milman type for certain convex sets of functions operators
Sufficient conditions are given in order that, for a bounded closed convex subset of a locally convex space , the set of continuous functions from the compact space into , is the uniformly closed convex hull in of its extreme points. Applications are made to the unit ball of bounded (or compact, or weakly compact) operators from certain Banach spaces into .
Theorems of ε-pseudoorthogonal decomposition in normed linear spaces.
Thin-shell concentration for convex measures
We prove that for s < 0, s-concave measures on ℝⁿ exhibit thin-shell concentration similar to the log-concave case. This leads to a Berry-Esseen type estimate for most of their one-dimensional marginal distributions. We also establish sharp reverse Hölder inequalities for s-concave measures.
Thompson isometries on positive operators: the 2-dimensional case.
Three Spaces Problem for Lyapunov Theorem on Vector Measure
It is proved that a Banach space X has the Lyapunov property if its subspace Y and the quotient space X/Y have it.
Three-space problems and bounded approximation properties
Let be a commuting approximating sequence of the Banach space X leaving the closed subspace A ⊂ X invariant. Then we prove three-space results of the following kind: If the operators Rₙ induce basis projections on X/A, and X or A is an -space, then both X and A have bases. We apply these results to show that the spaces and have bases whenever Λ ⊂ ℤ and ℤ∖Λ is a Sidon set.
Three-space problems for the approximation property
It is shown that there is a subspace of for which is isomorphic to such that does not have the approximation property. On the other hand, for there is a subspace of such that does not have the approximation property (AP) but the quotient space is isomorphic to . The result is obtained by defining random “Enflo-Davie spaces” which with full probability fail AP for all and have AP for all . For , are isomorphic to .
Tight Embeddability of Proper and Stable Metric Spaces
We introduce the notions of almost Lipschitz embeddability and nearly isometric embeddability. We prove that for p ∈ [1,∞], every proper subset of Lp is almost Lipschitzly embeddable into a Banach space X if and only if X contains uniformly the ℓpn’s. We also sharpen a result of N. Kalton by showing that every stable metric space is nearly isometrically embeddable in the class of reflexive Banach spaces.
Tilings in topological spaces.
Topics on analytic sets
Topological and algebraic genericity of divergence and universality
We give general theorems which assert that divergence and universality of certain limiting processes are generic properties. We also define the notion of algebraic genericity, and prove that these properties are algebraically generic as well. We show that universality can occur with Dirichlet series. Finally, we give a criterion for the set of common hypercyclic vectors of a family of operators to be algebraically generic.
Topological balls
Topological dual of with application to stochastic systems on Hilbert space
In this paper, we prove that the topological dual of the Banach space of bounded measurable functions with values in the space of nuclear operators, furnished with the natural topology, is isometrically isomorphic to the space of finitely additive linear operator-valued measures having bounded variation in a Banach space containing the space of bounded linear operators. This is then applied to a stochastic structural control problem. An optimal operator-valued measure, considered as the structural...