Applications of Berezin symbols in summability theory and related problems

Abstract

In this article, using the reproducing kernel and Berezin symbol techniques we prove that a sequence is Cesàro convergent, then it is Abel convergent. We prove criteria for Borel convergence of some sequences and series of complex numbers. Also, we answer if the Berezin transform of a bounded operator on the Dirichlet space D and the Fock space F(C) have radial limits almost everywhere. Moreover, we give an approximation problem for inner function by Berezin number of operators.