(e)-convergence and related problem

We answer negatively to a question of Zorboska (2003) [13] which is concerned to the boundary behavior of Berezin symbols of Bergman space operators We also introduce the notions of (e)-summability of sequences and series of complex numbers and study some of their properties As a corollary we obtain the classical Abel theorems of summability theory (C) 2010 Academie des sciences Published by Elsevier Masson SAS All rights reserved