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On the Comparison of Approximation Processes in Hilbert Spaces

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Linear Operators and Approximation / Lineare Operatoren und Approximation

Abstract

In two papers Jean Favard [16, 17] suggested the study of the comparison of approximation processes in Banach spaces. We pick up this problem in the case of Hilbert spaces. Strictly speaking we will deal with the following problem: Let H be an arbitrary (real or complex) Hilbert space, [H] the set of all bounded linear operators on H into itself. Let Г be an index set of real numbers with accumulation point + ∞ and T y ; γ ∈ Г c [H] be a strong approximation process, i.e., the operators T y are uniformly bounded and

$$\matrix{ {\mathop {\lim }\limits_{y \to \infty } \left\| {{T_y}f - f} \right\| = 0} & {\left( {f \in H} \right).} \cr } $$
(1.1)

.

The research of this author was supported by the “Landesamt für Forschung bei dem Minister für Wissenschaft und Forschung des Landes Nordrhein—Westfalen” Grant No. A/3-4379. Thanks are due to the Landesamt for permission to publish the results in these Proceedings.

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Authors and Affiliations

  1. Lehrstuhl a für Mathematik, Technische Hochschule Aachen, Germany

    P. L. Butzer, R. J. Nessel & W. Trebels

Authors
  1. P. L. Butzer
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  2. R. J. Nessel
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  3. W. Trebels
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Editor information

Editors and Affiliations

  1. Aachen, Germany

    P. L. Butzer

  2. Paris, France

    J.-P. Kahane

  3. Szeged, Hungary

    B. Szökefalvi-Nagy

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Butzer, P.L., Nessel, R.J., Trebels, W. (1972). On the Comparison of Approximation Processes in Hilbert Spaces. In: Butzer, P.L., Kahane, JP., Szökefalvi-Nagy, B. (eds) Linear Operators and Approximation / Lineare Operatoren und Approximation. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 20. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7283-6_21

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  • DOI: https://doi.org/10.1007/978-3-0348-7283-6_21

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-7285-0

  • Online ISBN: 978-3-0348-7283-6

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