Proceedings of the American Mathematical Society

Sequential type Korovkin theorem on $L^\infty$ for $\textbf {QC}$ -test functions

Author(s): Keiji Izuchi
Journal: Proc. Amer. Math. Soc. 125 (1997), 1153-1159.
MSC (1991): Primary 41J35, 46J10
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Abstract: Let $\{ T_n \}_n$ be a sequence of bounded linear operators on $L^\infty$ such that $\| T_n \| \to 1$ and $\| T_n g - g \|_\infty \to 0$ for every $g \in QC$ . It is proved that $\| T_n f - f \|_\infty \to 0$ for every $f \in L^\infty$ .

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 41J35, 46J10

Keiji Izuchi
Affiliation: Department of Mathematics, Niigata University, Niigata 950-21, Japan
Email: izuchi@scux.sc.niigata-u.ac.jp

DOI: 10.1090/S0002-9939-97-03884-7
PII: S 0002-9939(97)03884-7
Received by editor(s): February 23, 1996
Communicated by: Theodore W. Gamelin
Copyright of article: Copyright 1997, American Mathematical Society

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