Best N-Simultaneous Approximation in Lp(μ,X)

Let X be a Banach space. Let 1≤p<∞ and denote by Lp(μ,X) the Banach space of all X-valued Bochner p-integrable functions on a certain positive complete σ-finite measure space (Ω,Σ,μ), endowed with the usual p-norm. In this paper, the theory of lifting is used to prove that, for any weakly compact...

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Main Author: Tijani Pakhrou
Format: Article
Language:English
Published: Wiley 2017-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2017/7347130
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author Tijani Pakhrou
author_facet Tijani Pakhrou
author_sort Tijani Pakhrou
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description Let X be a Banach space. Let 1≤p<∞ and denote by Lp(μ,X) the Banach space of all X-valued Bochner p-integrable functions on a certain positive complete σ-finite measure space (Ω,Σ,μ), endowed with the usual p-norm. In this paper, the theory of lifting is used to prove that, for any weakly compact subset W of X, the set Lp(μ,W) is N-simultaneously proximinal in Lp(μ,X) for any arbitrary monotonous norm N in Rn.
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spelling doaj-art-96f7314a8aec413a8f32ba197705fc8f2025-08-20T02:09:51ZengWileyJournal of Function Spaces2314-88962314-88882017-01-01201710.1155/2017/73471307347130Best N-Simultaneous Approximation in Lp(μ,X)Tijani Pakhrou0Department of Mathematics, Faculty of Sciences, University of Alicante, 03080 Alicante, SpainLet X be a Banach space. Let 1≤p<∞ and denote by Lp(μ,X) the Banach space of all X-valued Bochner p-integrable functions on a certain positive complete σ-finite measure space (Ω,Σ,μ), endowed with the usual p-norm. In this paper, the theory of lifting is used to prove that, for any weakly compact subset W of X, the set Lp(μ,W) is N-simultaneously proximinal in Lp(μ,X) for any arbitrary monotonous norm N in Rn.http://dx.doi.org/10.1155/2017/7347130
spellingShingle Tijani Pakhrou
Best N-Simultaneous Approximation in Lp(μ,X)
Journal of Function Spaces
title Best N-Simultaneous Approximation in Lp(μ,X)
title_full Best N-Simultaneous Approximation in Lp(μ,X)
title_fullStr Best N-Simultaneous Approximation in Lp(μ,X)
title_full_unstemmed Best N-Simultaneous Approximation in Lp(μ,X)
title_short Best N-Simultaneous Approximation in Lp(μ,X)
title_sort best n simultaneous approximation in lp μ x
url http://dx.doi.org/10.1155/2017/7347130
work_keys_str_mv AT tijanipakhrou bestnsimultaneousapproximationinlpmx