Korovkin-type approximation for non-positive operators

The classical Korovkin theorem traditionally relies on the positivity of the underlying sequence of operators. However, in 1968, D. E. Wulbert established the first non-positive version. In this article, we generalize Wulbert’s result to the class of uniformly bounded sequence of operators. As an application, we obtain an operator version of this Korovkin-type theorem which will cover existing results in this direction. We also present illustrative examples, one of which has its roots in the Grunwald’s interpolation operator. In this context, we also present a direct approach with numerical illustrations.