Selfadjoint operator Korovkin type theorems and polynomial direct approximations with rates

Here we present self adjoint operator Korovkin type theorems, via self adjoint operator Shisha-Mond type inequalities, also we give self adjoint operator polynomial approximations. This is a quantitative treatment to determine the degree of self adjoint operator uniform approximation with rates, of sequences of self adjoint operator positive linear operators. The same kind of work is performed over important operator polynomial sequences. Our approach is direct based on Gelfand isometry.