Discrete approximating operators on function algebras
Let \(T\) be the unit circle and let \(A(T)\) be the disk algebra. For linear operators \(L_ n: A(T)\to A(T)\) of the form \(L_ n f=\sum_{k=1}^ n f(z_{n,k}\ell_{n,k}\), where \(z_{n,k}\in T\) and \(\ell_{n,k}\in A(T)\), \textit{G. Somorjai} [Constructive function theory, Proc. int. Conf., Blagoevgrad 1977, 489-496 (1980; Zbl 0396.41009)] proved that there exists a function \(f\in A(T)\) such that \(L_ nf\) does not converge to \(f\). The author gives a new presentation and various extensions of the cited theorem.
scientific article; zbMATH DE number 61196
scientific article