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Weak Chebyshev subspaces and $ A$-subspaces of $ C[a,b]$


Author: Wu Li
Journal: Trans. Amer. Math. Soc. 322 (1990), 583-591
MSC: Primary 41A50; Secondary 41A52
DOI: https://doi.org/10.1090/S0002-9947-1990-1010886-6
MathSciNet review: 1010886
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Abstract: In this paper we show some very interesting properties of weak Chebyshev subspaces and use them to simplify Pinkus's characterization of $ A$subspaces of $ C[a,b]$. As a consequence we obtain that if the metric projection $ {P_G}$ from $ C[a,b]$ onto a finite-dimensional subspace $ G$ has a continuous selection and elements of $ G$ have no common zeros on $ (a,b)$, then $ G$ is an $ A$-subspace.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1990-1010886-6
Keywords: $ A$-subspace, weak Chebyshev subspace, Chebyshev subspace, metric projection, continuous metric selection
Article copyright: © Copyright 1990 American Mathematical Society

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