Chebyshev subspaces and convergence of positive linear operators

Micchelli, C. A.

doi:10.1090/S0002-9939-1973-0328445-2

Chebyshev subspaces and convergence of positive linear operators
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by C. A. Micchelli PDF

Proc. Amer. Math. Soc. 40 (1973), 448-452 Request permission

Abstract:

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

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