A Korovkin Theorem for Abstract Lebesgue Spaces

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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Zusammenfassung: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.
ISSN:0021-9045
1096-0430
DOI:10.1006/jath.1999.3377