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.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- 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