On almost Chebyshev subspaces |
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Authors: | Ka-Sing Lau |
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Institution: | Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 U.S.A. |
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Abstract: | A closed subspace F in a Banach space X is called almost Chebyshev if the set of x ε X which fail to have unique best approximation in F is contained in a first category subset. We prove, among other results, that if X is a separable Banach space which is either locally uniformly convex or has the Radon-Nikodym property, then “almost all” closed subspaces are almost Chebyshev. |
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