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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Chebyshev subspaces and convergence of positive linear operators


Author: C. A. Micchelli
Journal: Proc. Amer. Math. Soc. 40 (1973), 448-452
MSC: Primary 41A65
DOI: https://doi.org/10.1090/S0002-9939-1973-0328445-2
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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DOI: https://doi.org/10.1090/S0002-9939-1973-0328445-2
Keywords: Chebyshev subspace, positive operators, Korovkin's theorem
Article copyright: © Copyright 1973 American Mathematical Society