Proximinality in L-p(mu,X).



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Mendoza Casas, José (1998) Proximinality in L-p(mu,X). Journal of Approximation Theory, 93 (2). pp. 331-343. ISSN 0021-9045

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Let X be a Banach space and let Y be a closed subspace of X. Let 1 less than or equal to p less than or equal to infinity and let us denote by L-p(mu, X) the Banach space of all X-valued Bochner p-integrable (essentially bounded for p = infinity) functions on a certain positive complete sigma-finite measure space (Omega, Sigma, mu), endowed with the usual p-norm. In this paper we give a negative answer to the following question: "If Y is proximinal in X, is L-p(mu, Y) proximinal in L-p(mu, X)?" We also show that the answer is affirmative for separable spaces Y. Some consequences of this are obtained.

Item Type:Article
Uncontrolled Keywords:proximinal subspaces; best approximation in Lp (μ,X).
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16870
Deposited On:25 Oct 2012 08:05
Last Modified:26 Jul 2018 07:00

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