Proximinality in L-p(mu,X).
| dc.contributor.author | Mendoza Casas, José | |
| dc.date.accessioned | 2023-06-20T17:01:47Z | |
| dc.date.available | 2023-06-20T17:01:47Z | |
| dc.date.issued | 1998-05-02 | |
| dc.description.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. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | D.G.I.C.Y.T. | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/16870 | |
| dc.identifier.doi | 10.1006/jath.1997.3163 | |
| dc.identifier.issn | 0021-9045 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0021904597931634 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57653 | |
| dc.issue.number | 2 | |
| dc.journal.title | Journal of Approximation Theory | |
| dc.language.iso | eng | |
| dc.page.final | 343 | |
| dc.page.initial | 331 | |
| dc.publisher | Academic Press-Elsevier Science | |
| dc.relation.projectID | PB94-0243. | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.keyword | proximinal subspaces | |
| dc.subject.keyword | best approximation in Lp (μ | |
| dc.subject.keyword | X). | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Proximinality in L-p(mu,X). | |
| dc.type | journal article | |
| dc.volume.number | 93 | |
| dcterms.references | W. Deeb and R. Khalil, Best approximation in L(X, Y), Math. Proc. Cambridge Philos. Soc. 104 (1988), 527-531. J. Diestel and J. J. Uhl Jr., ``Vector Measures,'' Math. Surveys, Vol. 15, Amer. Math. Soc., Providence, 1977. R. Holmes and B. Kripke, Smoothness of approximation, Michigan Math. J. 15 (1968), 225-248. Zhibao Hu and Bor-Luh Lin, Extremal structure of the unit ball of Lp(+, X)*, J. Math. Anal. Appl. 200 (1996), 567-590. R. Khalil, Best approximation in Lp(I, X), Math. Proc. Cambridge Philos. Soc. 94 (1983), 277-279. R. Khalil and W. Deeb, Best approximation in Lp(I, X), II, J. Approx. Theory 59 (1989), 296-299. R. Khalil and F. Saidi, Best approximation in L1(I, X), Proc. Amer. Math. Soc. 123 (1995), 183-190. W. A. Light, Proximinality in Lp(S, Y), Rocky Mountain J. Math. 19 (1989), 251-259. W. A. Light and E. W. Cheney, Some best approximation theorems in tensor product spaces, Math. Proc. Cambridge Philos. Soc. 89 (1981), 385-390. W. A. Light and E. W. Cheney, ``Approximation Theory in Tensor Product Spaces,'' Lecture Notes in Math., Vol. 1169, Springer-Verlag, New York, 1985. F. B. Saidi, On the smoothness of the metric projection and its applications to proximinality in Lp(S, Y), J. Approx. Theory 83 (1995), 205-219. You Zhao-Yong and Guo Tie-Xin,Pointwise best approximation in the space of strongly measurable functions with applications to best approximation in Lp(+, X),J.Approx. Theory 78 (1994), 314-320. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 3fdf00ed-ed02-482c-a736-bb87c2753a89 | |
| relation.isAuthorOfPublication.latestForDiscovery | 3fdf00ed-ed02-482c-a736-bb87c2753a89 |
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