A discrete Korovkin theorem and BKW-operators (Q1912241)

Using the idea of Stone-Cech compactification, the paper gives a new simple proof for a discrete Korovkin theorem, independingly considered by \textit{G. A. Anastassiou} [J. Approximation Theory 61, No. 3, 384-386 (1990; Zbl 0722.41025)] and \textit{R. Sato} [J. Approximation Theory 64, No. 2, 235-237 (1991; Zbl 0722.41026)]. Moreover, a generalization of this theorem is presented, implying some information on local unital linear contractions on the Banach space of bounded complex-valued functions \(B(X)\) on an arbitrary set \(X\). These contractions, called BKW-operators on \(B(X)\), are investigated for a finite collection of test functions with a suitable property and a seminorm defined by a finite subset of \(X\). Some examples illustrate the presented theory.