A Korovkin Theorem for Abstract Lebesgue Spaces

Wulbert and Meir have each obtained a Korovkin theorem for weak convergence of operators on an L1 space. Here we prove a result which includes both of these theorems and which provides a general setting for weak Korovkin type L1 convergence of operators which are not assumed positive.

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Veröffentlicht in:	Journal of approximation theory 2000-01, Vol.102 (1), p.13-20
1. Verfasser:	Renaud, Peter
Format:	Artikel
Sprache:	eng
Schlagworte:	abstract Lebesgue lattices Korovkin weak convergence
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description	Wulbert and Meir have each obtained a Korovkin theorem for weak convergence of operators on an L1 space. Here we prove a result which includes both of these theorems and which provides a general setting for weak Korovkin type L1 convergence of operators which are not assumed positive.
doi_str_mv	10.1006/jath.1999.3377
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source	Elsevier ScienceDirect Journals Complete; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals
subjects	abstract Lebesgue lattices Korovkin weak convergence
title	A Korovkin Theorem for Abstract Lebesgue Spaces
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