ANOTHER LOOK AT VORONOVSKAJA TYPE FORMULAS

Voronovskaja type formulas are usually established for sequences of positive linear operators, i.e, operators P-n with P(n)f >= 0 whenever the function f is positive. The aim of this paper is twofold. First, we obtain some general formulas concerning compositions of operators on Banach spaces, without any assumption of positivity. Next, we establish Voronovskaja type formulas for operators which are manifestly nonpositive. Combining these two approaches we recover some known results and obtain new applications. The final section is devoted to inequalities accompanying our formulas.