Contre-exemple à la propriété d'approximation uniforme dans les espaces de Banach
Convergence des martingales pluri-sous-harmoniques vectorielles à deux indices
Convergence of convex functions and generalized inf-convolutive approximations. (Convergences des fonctions convexes et approximations inf-convolutives généralisées.)
Convergence of greedy approximation I. General systems
We consider convergence of thresholding type approximations with regard to general complete minimal systems eₙ in a quasi-Banach space X. Thresholding approximations are defined as follows. Let eₙ* ⊂ X* be the conjugate (dual) system to eₙ; then define for ε > 0 and x ∈ X the thresholding approximations as , where . We study a generalized version of that we call the weak thresholding approximation. We modify the in the following way. For ε > 0, t ∈ (0,1) we set and consider the weak...
Convergence of series and isomorphic embeddings in Banach spaces
Convergence of Taylor series in Hardy and Besov spaces.
Convergence of the dual greedy algorithm in Banach spaces.
Convergence of Tight Asymptotic Martingales in a Banach Space.
Convergence theorems for generalized projections and maximal monotone operators in Banach spaces.
Convex cones in finite-dimensional real vector spaces
Convex functions with non-Borel set of Gâteaux differentiability points
We show that on every nonseparable Banach space which has a fundamental system (e.gȯn every nonseparable weakly compactly generated space, in particular on every nonseparable Hilbert space) there is a convex continuous function such that the set of its Gâteaux differentiability points is not Borel. Thereby we answer a question of J. Rainwater (1990) and extend, in the same time, a former result of M. Talagrand (1979), who gave an example of such a function on .
Convex sets in Banach spaces and a problem of Rolewicz
Let be the set of all closed, convex and bounded subsets of a Banach space X equipped with the Hausdorff metric. In the first part of this work we study the density character of and investigate its connections with the geometry of the space, in particular with a property shared by the spaces of Shelah and Kunen. In the second part we are concerned with the problem of Rolewicz, namely the existence of support sets, for the case of spaces C(K).
Convex transformations with Banach lattice range.
A closed epigraph theorem for Jensen-convex mappings with values in Banach lattices with a strong unit is established. This allows one to reduce the examination of continuity of vector valued transformations to the case of convex real functionals. In particular, it is shown that a weakly continuous Jensen-convex mapping is continuous. A number of corollaries follow; among them, a characterization of continuous vector-valued convex transformations is given that answers a question raised by Ih-Ching...
Convexités uniformes et inégalités de martingales.
Convexity and Reflexivity
Convexity around the Unit of a Banach Algebra
2000 Mathematics Subject Classification: Primary: 46B20. Secondary: 46H99, 47A12.We estimate the (midpoint) modulus of convexity at the unit 1 of a Banach algebra A showing that inf {max±||1 ± x|| − 1 : x ∈ A, ||x||=ε} ≥ (π/4e)ε²+o(ε²) as ε → 0. We also give a characterization of two-dimensional subspaces of Banach algebras containing the identity in terms of polynomial inequalities.
Convexity conditions in normed linear spaces.
Convexity, type and three space problem
Convolution of Operators and Applications.
Copies of C0 in Certain Vector-Valued Function Banach Spaces.