Convergent sequences of linear operators in semiordered spaces

The definition given by P. P. Korovkin of operators of the class $S_m$ and conditions for the convergence of these operators to the identity operator are extended to apply to regular operators from a $K$-space $R_0$ with a unit, into a $K$-space $R_1$, where $R_0$ and $R_1$ are normally contained in the union of the spaces $S[a,b]$ and $s$.