The operator remainder in the Euler-Maclaurin formula.
The space of all bounded operators on Hilbert space does not have the approximation property
The strong unicity constant and its applications
In this report we discuss the applications of the strong unicity constant and highlight its use in the minimal projection problem.
The strong unicity constant for projections.
Tractability of multivariate problems for weighted spaces of functions
We survey recent results on tractability of multivariate problems. We mainly restrict ourselves to linear multivariate problems studied in the worst case setting. Typical examples include multivariate integration and function approximation for weighted spaces of smooth functions.
Transitivity of proximinality and norm attaining functionals
We study the question of when the set of norm attaining functionals on a Banach space is a linear space. We show that this property is preserved by factor reflexive proximinal subspaces in spaces and generally by taking quotients by proximinal subspaces. We show, for (ℓ₂) and c₀-direct sums of families of reflexive spaces, the transitivity of proximinality for factor reflexive subspaces. We also investigate the linear structure of the set of norm attaining functionals on hyperplanes of c₀ and...
Tres teoremas de aproximación en el espacio Lp mediante polinomios de coeficientes enteros.
Two-dimensional real symmetric spaces with maximal projection constant
Let V be a two-dimensional real symmetric space with unit ball having 8n extreme points. Let λ(V) denote the absolute projection constant of V. We show that where is the space whose ball is a regular 8n-polygon. Also we reprove a result of [1] and [5] which states that for any two-dimensional real symmetric space V.
Über die Charakterisierung von ...(X) durch eien optimalen Satz vom Korovkintyp.
Über die Korovkinhülle von Teilmengen in lokalkonvexen Vektorverbänden.
Über Korovkin-Sätze in lokalkonvexen Vektorverbänden.
Ultrasymmetric sequence spaces in approximation theory.
Let φ(t) be a positive increasing function and let Ê be an arbitrary sequence space, rearrangement-invariant with respect to the atomic measure µ(n) = 1/n. Let {an*} mean the decreasing rearrangement of a sequence {|an|}. A sequence space lφ,E with symmetric (quasi)norm || {φ(n)an*} ||Ê is called ultrasymmetric, because it is not only intermediate but also interpolation between the corresponding Lorentz and Marcinkiewicz spaces Λφ and Mφ. We study properties of the spaces lφ,E for all admissible...
Un procédé itératif avec l'opérateur modifie et les problèmes d'approximation
Unicity of Best One-Sided L1-Approximations
Uniform approximation by minimum norm interpolation.
Uniform approximation by real functions
Uniform extension of linear functionals
Uniqueness of minimal projections onto two-dimensional subspaces
We prove that minimal projections from (1 < p < ∞) onto any two-dimensional subspace are unique. This result complements the theorems of W. Odyniec ([OL, Theorem I.1.3], [O3]). We also investigate the minimal number of norming points for such projections.
Universal approximations of certain functionals in Banach spaces
Universal simultaneous approximations of the coefficient functionals