Complemented copies of L1 in Lp(μ;E).
| dc.contributor.author | Mendoza Casas, José | |
| dc.date.accessioned | 2023-06-20T17:01:56Z | |
| dc.date.available | 2023-06-20T17:01:56Z | |
| dc.date.issued | 1992-05 | |
| dc.description.abstract | Let E be a Banach space, let (OMEGA, SIGMA, mu) a finite measure space, let 1 < p < infinity and let L(p)(mu; E) the Banach space of all E-valued p-Bochner mu-integrable functions with its usual norm. In this note it is shown that E contains a complemented subspace isomorphic to l1 if (and only if ) L(p)(mu; E) does. An extension of this result is also given. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGICYT | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/16886 | |
| dc.identifier.doi | 10.1017/S0305004100075605 | |
| dc.identifier.issn | 0305-0041 | |
| dc.identifier.officialurl | http://journals.cambridge.org/abstract_S0305004100075605 | |
| dc.identifier.relatedurl | http://journals.cambridge.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57657 | |
| dc.issue.number | 3 | |
| dc.journal.title | Mathematical Proceedings of the Cambridge Philosophical Society | |
| dc.language.iso | eng | |
| dc.page.final | 534 | |
| dc.page.initial | 531 | |
| dc.publisher | Cambridge Univ Press | |
| dc.relation.projectID | PB88-0141 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.982.2 | |
| dc.subject.keyword | block sequence | |
| dc.subject.keyword | finite measure space | |
| dc.subject.keyword | complemented subspace | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Complemented copies of L1 in Lp(μ;E). | |
| dc.type | journal article | |
| dc.volume.number | 111 | |
| dcterms.references | Bombal, F.. On l1, subspaces of Orlicz vector-valued function spaces. Math. Proc. Cambridge Philos. Soc. 101 (1987), 107–112. Bombal, F.. On embedding l1 as a complemented subspace of Orlicz vector valued function spaces. Rev. Mat. Univ. Complutense Madrid 1 (1988), 13–17. Bombal, F.. On (V*) sets and Pelczynski's property (V*). Glasgow Math. J. 32 (1990), 109–120. Bourgain, J.. New classes of Lp-spaces. Lecture Notes in Math. vol. 889 (Springer-Verlag, 1981). Diestel, J.. Sequences and Series in Banach spaces. Graduate Texts in Math. no. 92 (Springer-Verlag, 1984). Diestel, J. and Uhl, J. J. Jr. Vector Measures. Math. Surveys no. 15 (American Mathematical Society, 1977). A. and C. IONESCU TUXCEA. Topics in the Theory of Liftings. Ergebnisse der Mathematik und ihrer Grenzgebiete vol. 48 (Springer-Verlag, 1969). Lindenstauss, J. and Tzafriri, L.. Classical Banach spaces, vol. 1. Ergebnisse der Mathematik und ihrer Grenzgebiete vol. 92 (Springer-Verlag, 1977). Lindenstauss, J. and Tzafriri, L.. Classical Banach spaces, vol. 2. Ergebnisse der Mathematik und ihrer Grenzgebiete vol. 97 (Springer-Verlag, 1979). Pisier, G.. Une proprieté de stabilité de la classe des espaces ne contenant pas l1. C.R. Acad. Sci. Paris Sér. A 286 (1978), 747–749. Talagrand, M.. Weak Cauchy sequences in L1(E). Amer. J. Math. 106 (1984), 703–724. Tzafriri, L.. Reflexivity in Banach lattices and their subspaces. J. Funct. Anal. 10 (1972), 1–18. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 3fdf00ed-ed02-482c-a736-bb87c2753a89 | |
| relation.isAuthorOfPublication.latestForDiscovery | 3fdf00ed-ed02-482c-a736-bb87c2753a89 |
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