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Proximinality of certain subspaces of $C_b(S;E)$

1989
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Rocky Mountain Journal of Mathematics
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Throughout this paper, 5 is a completely regular HausdorfF space and E is a Banach space. The vector space of all continuous and bounded functions / : S -• E, denoted by Cb(S;E), is equipped with the supnorm ||/|| = sup{||/(x)||;xG5}. Recall that a closed subpsace V of a Banach space E is said to be proximinal if every a G E admits a best approximant from V', i.e., a point v G V for which The set of best approximants to a from V is denoted by Py(a), and the set-valued mapping a -• Py(a) is

doi:10.1216/rmj-1989-19-1-335
fatcat:ccs2xd66ebg53jogv4kvg64xcy