The Hereditary Dunford-Pettis Property On C(K,E)
| dc.contributor.author | Cembranos Díaz, María Del Pilar | |
| dc.date.accessioned | 2023-06-21T02:01:33Z | |
| dc.date.available | 2023-06-21T02:01:33Z | |
| dc.date.issued | 1987 | |
| dc.description.abstract | The author studies the hereditary Dunford-Pettis property for spaces CX(K) of continuous Xvalued functions (X a Banach space) on a compact Hausdorff space K. First, she shows that CX(K) has the hereditary Dunford-Pettis property if and only if one of the following holds: (a) K is finite andX has the hereditary Dunford-Pettis property; (b) C(K) and c0(X) have the hereditary Dunford-Pettis property. Unwilling to give up here, the author provides an elegant characterization of when c0(X) has the hereditary Dunford-Pettis property. Since the paper was written, Nunez has provided an elegant example (based on work of Talagrand) of an X such that, while X is hereditarily Dunford-Pettis, c0(X) is not. Remarkable and satisfying! | en |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | The Board Of Trustees Of The University Of Illinois | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/14928 | |
| dc.identifier.issn | 0019-2082 | |
| dc.identifier.officialurl | http.://dx.doi.org/10.2307/2044800 | |
| dc.identifier.relatedurl | http://projecteuclid.org/euclid.ijm/1256069289 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/64613 | |
| dc.issue.number | 3 | |
| dc.journal.title | Illinois Journal of Mathematics | |
| dc.language.iso | eng | |
| dc.page.final | 373 | |
| dc.page.initial | 365 | |
| dc.publisher | University of Illinois | |
| dc.relation.projectID | Supported In Part By CAICYT Grant 0338-84 (España). | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 517 | |
| dc.subject.keyword | Mathematics | |
| dc.subject.ucm | Análisis matemático | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.subject.unesco | 1202 Análisis y Análisis Funcional | |
| dc.title | The Hereditary Dunford-Pettis Property On C(K,E) | en |
| dc.type | journal article | |
| dc.volume.number | 31 | |
| dcterms.references | 1. J. DIESTEL, A survey of results related to the Dunford-Pettis property, Contemporary Mathematics, vol. 2 (1980), pp. 15-60. 2. I. DOBIKOV, On representation of linear operators on Co(T, X), Czech. Math. J., vol. 21 (1971), pp. 13-30. 3. A. GROTHENDIV.CK, Sur les applications lin$.aires faiblement compactes d’espaces du type C( K), Canad, J. Math., vol. 5 (1953), pp. 129-173. 4. J. HAGLV.I, A counterexample to several questions about Banach spaces, Studia Math., vol..,55 (1977), pp. 289-308. 5. J. LINDENSTRAUSS and L. TZAFRIRI, Classical Banach Spaces I, Springer-Verlag, New York, 1977. 6. A. PLCZYNSrd and W. SZUNK, An example of a non-shrinking basis, Rev. Roumaine Math. Pures Appl., vol. 10 (1965), pp. 961-966. 7. Z. S.MADNL Banach spaces of continuous functions, PWN, Warsaw 1971. 8. M. TAtSRAND, The Dunford-Pettis property in C([0,1], E)and LX(E), Israel J. Math., vol. 44 (1983), pp. 317-321. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | a09c0500-e6a7-40f8-beeb-85fc6a870c2d | |
| relation.isAuthorOfPublication.latestForDiscovery | a09c0500-e6a7-40f8-beeb-85fc6a870c2d |
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