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

Author: Keiji Izuchi
Journal: Proc. Amer. Math. Soc. 125 (1997), 1153-1159
MSC (1991): Primary 41J35, 46J10
MathSciNet review: 1396982
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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 $.

References [Enhancements On Off] (What's this?)

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Additional Information

Keiji Izuchi
Affiliation: Department of Mathematics, Niigata University, Niigata 950-21, Japan

Received by editor(s): February 23, 1996
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1997 American Mathematical Society

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