Sätze vom Bohman-Korovkin-Typ für lokalkonvexe Vektorverbände

Bohman–Korovkin type theorems for locally convex vector lattices

Authors

  • Heiner Gonska University of Duisburg-Essen, Germany

DOI:

https://doi.org/10.33993/jnaat441-1061

Keywords:

Korovkin-type theorem, approximation of lattice homomorphisms, positive linear operators, Banach function spaces.
Abstract views: 300

Abstract

Two Korovkin-type theorems inspired by the work of Scheffold are given concerning the approximation of a continuous lattice homomorphism \(P\) by a sequence of certain positive linear operators \(T_n\). The first result is used to prove a generalization of a proposition of Muller dealing with approximation in Banach function spaces.

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Author Biography

Heiner Gonska, University of Duisburg-Essen, Germany

Faculty of Mathematics

References

H. Berens, und G.G. Lorentz, Theorem of Korovkin Type for Positive Linear Operators on Banach Lattices, Approximation Theory, G.G. Lorentz, Ed., New York - London: Academic Press, (1973), pp. 1–30.

H. Gonska, Konvergenzsätze von Bohman-Korovkin-Typ für positive lineare Operatoren, Diplomarbeit, Ruhr-Universität Bochum, 1975.

M.W. Müller, Sätze vom Bohman-Korowkin-Typ für Banachsche Funktionenräume, Linear Operators and Approximation, P.L. Butzer, J.-P. Kahane und B. Sz.-Nagy, Ed., Basel-Stuttgart: Birkhäuser, (1972), pp. 292–299, https://doi.org/10.1007/978-3-0348-7283-6_26 DOI: https://doi.org/10.1007/978-3-0348-7283-6_26

E. Scheffold, Ein al lgemeiner Korovkin-Satz für lokalkonvexe Vektorverbände, Math. Z., 132 (1973), pp. 209–214, https://doi.org/10.1007/BF01213865 DOI: https://doi.org/10.1007/BF01213865

M. Wolff, Darstel lung von Banach-Verbänden und Sätze vom Korovkin-Typ, Math. Ann., 200 (1973), pp. 47–67, https://doi.org/10.1007/BF01578291 DOI: https://doi.org/10.1007/BF01578291

M. Wolff, Uber Korovkin-Sätze in lokalkonvexen Vektorverbänden, Math. Ann, 204 (1973), pp. 44–56, https://doi.org/10.1007/BF01431487 DOI: https://doi.org/10.1007/BF01431487

M. Wolff, A General Theorem of Korovkin Type for Vector Lattices, Approximation Theory, G.G. Lorentz, Ed., New York - London: Academic Press, (1973), pp. 517–521.

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Published

2015-12-18

How to Cite

Gonska, H. (2015). Sätze vom Bohman-Korovkin-Typ für lokalkonvexe Vektorverbände: Bohman–Korovkin type theorems for locally convex vector lattices. J. Numer. Anal. Approx. Theory, 44(1), 62–68. https://doi.org/10.33993/jnaat441-1061

Issue

Vol. 44 No. 1 (2015)

Section

Articles

License

Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

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