Directions d'uniforme convexité dans un espace normé
Dispersed Chebyshev Sets and Coverings by Balls.
Duality, reflexivity and atomic decompositions in Banach spaces
We study atomic decompositions and their relationship with duality and reflexivity of Banach spaces. To this end, we extend the concepts of "shrinking" and "boundedly complete" Schauder basis to the atomic decomposition framework. This allows us to answer a basic duality question: when an atomic decomposition for a Banach space generates, by duality, an atomic decomposition for its dual space. We also characterize the reflexivity of a Banach space in terms of properties of its atomic decompositions....
Ein Funktionstheoretischer Beweis des Satzes von Müntz.
Ein Satz vom Korovkin-Typ für Ck-Räume.
Eindeutigkeit in der L1-Approximation.
Embedding theorems for a class of functions.
Embeddings of Besov spaces of logarithmic smoothness
This paper deals with Besov spaces of logarithmic smoothness formed by periodic functions. We study embeddings of into Lorentz-Zygmund spaces . Our techniques rely on the approximation structure of , Nikol’skiĭ type inequalities, extrapolation properties of and interpolation.
Equilateral, diametral, centered sets and subsets of spheres.
Equivalence, unconditionality and convergence a.e. of the spline bases in spaces
Erratum to the paper "On the Kaczmarz algorithm of approximation in infinite-dimensional spaces" (Studia Math. 148 (2001), 75-86)
Existence of best approximations
Extended Chebyshev systems for the expansions of exp (At).
Extending Stechkin's theorem and beyond.
Extensions of best approximation and coincidence theorems.
Extensions of linear operators from hyperplanes of
Let be a hyperplane and let be given. Denote In this paper the problem of calculating of the constant is studied. We present a complete characterization of those for which . Next we consider the case . Finally some computer examples will be presented.
Farthest points in normed linear spaces.
For a dense set of equivalent norms, a non-reflexive Banach space contains a triangle with no Chebyshev center
Let be a non-reflexive real Banach space. Then for each norm from a dense set of equivalent norms on (in the metric of uniform convergence on the unit ball of ), there exists a three-point set that has no Chebyshev center in . This result strengthens theorems by Davis and Johnson, van Dulst and Singer, and Konyagin.
Formes linéaires invariantes par translation et approximation rationnelle