On certain operator classes which include the class of positive operators (Q1357946)

Let \(L_n: C([a,b]^m) \to C ([a,b]^m), n=1,2,\ldots\) be a certain class of operators (including the class of positive operators). In the article, a proof of an analogon of Korovkin's Theorem on convergence of \(L_n\) in the space of continuous functions of several variables is presented. In contrast with earlier results of the authors, a new approach is taken, which removes technical obstacles. Further, the rate of approximation of functions by operators \(L_n\) is estimated.