## 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