Mendoza Casas, Jose (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.
|Uncontrolled Keywords:||proximinal subspaces; best approximation in Lp (μ,X).|
|Subjects:||Sciences > Mathematics > Functional analysis and Operator theory|
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|Deposited On:||25 Oct 2012 10:05|
|Last Modified:||25 Oct 2012 10:05|
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