Chebyshev subspaces and convergence of positive linear operators

Abstract

A theorem of Korovkin states that a sequence of positive linear operators on C [ a , b ] C[a,b] converges strongly to the identity if and only if convergence holds on a three-dimensional Chebyshev subspace of C [ a , b ] C[a,b] . We extend this theorem to include Chebyshev subspaces of arbitrary dimension and convergence to other positive linear operators.