Sandwich theorems for operators of convex type (Q1343964)

This note centers around a class of operators from a real vector space into a Dedekind complete ordered real vector space, which satisfy the usual convexity inequalities only with respect to some given subset \(\Lambda\) of the unit interval. The author shows that between a \(\Lambda\)-concave and a \(\Lambda\)-convex operator one can always find a \(\Lambda\)-affine operator. He gives several applications of this sandwich principle.