𝒜 $$\mathcal{A}$$ -Summability of Sequences of Linear Conservative Operators

Abstract

This work deals with the approximation of functions by sequences of linear operators. Here the classical convergence is replaced by matrix summability. Beyond the usual positivity of the operators involved in the approximation processes, more general conservative approximation properties are considered. Quantitative results, as well as results on asymptotic formulae and saturation are stated. It is the intention of the authors to show the way in which some concepts of generalized convergence entered Korovkin-type approximation theory. This is a survey work that gathers and orders the results stated by the authors and other researchers within the aforesaid subject.