Sequential type Korovkin theorem on $L^\infty$ for QC-test functions
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- by Keiji Izuchi
- Proc. Amer. Math. Soc. 125 (1997), 1153-1159
- DOI: https://doi.org/10.1090/S0002-9939-97-03884-7
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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
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Bibliographic Information
- Keiji Izuchi
- Affiliation: Department of Mathematics, Niigata University, Niigata 950-21, Japan
- Email: izuchi@scux.sc.niigata-u.ac.jp
- Received by editor(s): February 23, 1996
- Communicated by: Theodore W. Gamelin
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1153-1159
- MSC (1991): Primary 41J35, 46J10
- DOI: https://doi.org/10.1090/S0002-9939-97-03884-7
- MathSciNet review: 1396982