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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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Official URL: http://www.sciencedirect.com/science/article/pii/S0021904597931634

## Abstract

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 |
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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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