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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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2017/7347130 |
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| _version_ | 1850210125552287744 |
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| author | Tijani Pakhrou |
| author_facet | Tijani Pakhrou |
| author_sort | Tijani Pakhrou |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-96f7314a8aec413a8f32ba197705fc8f |
| institution | OA Journals |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| 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 |