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Chebyshev subspaces and convergence of positive linear operators

Author: C. A. Micchelli
Journal: Proc. Amer. Math. Soc. 40 (1973), 448-452
MSC: Primary 41A65
MathSciNet review: 0328445
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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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Keywords: Chebyshev subspace, positive operators, Korovkin's theorem
Article copyright: © Copyright 1973 American Mathematical Society

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