A note on porosity and the Mazur intersection property
| dc.contributor.author | Jiménez Sevilla, María Del Mar | |
| dc.contributor.author | Moreno, José Pedro | |
| dc.date.accessioned | 2023-06-20T18:47:34Z | |
| dc.date.available | 2023-06-20T18:47:34Z | |
| dc.date.issued | 2000-12 | |
| dc.description | The authors wish to thank the C.E.C.M., the Department of Mathematics and Statistics of the Simon Fraser University and specially J. Borwein for their hospitality during the preparation of this note. We also thank the referee for valuable suggestions improving its readability | |
| dc.description.abstract | Let M be the collection of all intersections of balls, considered as a subset of the hyperspace H of all closed, convex and bounded sets of a Banach space, furnished with the Hausdorff metric. We prove that M is uniformly very porous if and only if the space fails the Mazur intersection property. | |
| 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/22175 | |
| dc.identifier.doi | 10.1112/S0025579300015874 | |
| dc.identifier.issn | 0025-5793 | |
| dc.identifier.officialurl | http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7015048 | |
| dc.identifier.relatedurl | http://journals.cambridge.org/action/login?sessionId=9C965789AD5BE3B591E6AECA8AF3884E.journals | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/58631 | |
| dc.issue.number | 1-2 | |
| dc.journal.title | Mathematika. A Journal of Pure and Applied Mathematics | |
| dc.language.iso | eng | |
| dc.page.final | 272 | |
| dc.page.initial | 267 | |
| dc.publisher | Cambridge Univ. Press | |
| dc.relation.projectID | PB 96-0607 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 512 | |
| dc.subject.keyword | Porosity | |
| dc.subject.keyword | Convex bodies | |
| dc.subject.keyword | Mazur intersection property | |
| dc.subject.ucm | Álgebra | |
| dc.subject.unesco | 1201 Álgebra | |
| dc.title | A note on porosity and the Mazur intersection property | |
| dc.type | journal article | |
| dc.volume.number | 47 | |
| dcterms.references | Donjian Chen and Bor-Luh Lin, Ball separation properties in Banach spaces, Rocky Mountain J.Math.,28(3) (1998), 835–873. Donjian Chen and Bor-Luh Lin, On B-convex and Mazur sets of Banach spaces, Bull. Polish Acad. Sci. Math. 43 (3) (1995), 191–198. F. S. De Blasi, J, Myjak and P. L. Papini, Porous sets in best approximation theory, J. Lond.Math.Soc., 44 (1) (1991), 135–142. R. Deville, G. Godefroy, and V. Zizler, Smoothness and renormings in Banach spaces, vol. 64, Pitman Monograph and Surveys in Pure and Applied Mathematics, 1993. R. Deville and J. Revalski, Porosity of ill-posed problems, Proc. Amer. Math. Soc., to appear. P. G. Georgiev, A. S. Granero, M. Jiménez Sevilla and J. P. Moreno, Mazur intersection properties and differentiability of convex functions in Banach spaces, J. Lond. Math. Soc., to appear. J. R. Giles, D. A. Gregory, and B. Sims, Characterization of normed linear spaces with Mazur’s intersection property, Bull. Austral. Math. Soc. 18 (1978), 471–476. P. M. Gruber, Baire categories in convexity, Handbook of convex geometry (P. M. Gruber and J. M. Wills eds.), North-Holland, 1993, 1327-1346. P. M. Gruber, The space of convex bodies, Handbook of convex geometry (P. M. Gruber and J. M. Wills eds.), North-Holland, 1993, 301-318. M. Jiménez Sevilla and J.P. Moreno, Renorming Banach spaces with the Mazur intersection property, J. Funct. Anal., 144 (2) (1997) 486–504. K. Kuratowski, Topology I, Academic Press, New York and London, 1966. S. Mazur, Über schwache Konvergentz in den Raumen Lp, Studia Math. 4 (1933), 128–133. R. R. Phelps, Convex functions, monotone operators and differentiability, Lecture Notes in Math. 1364, Springer Verlag, 1989; rev ed., 1993. D. Preiss and L. Zajicek, Stronger estimates of smallness of sets of Fréchet nondifferentiability of convex functions, Proc. 11th Winter School,Suppl. Rend. Circ. Mat. di Palermo, Ser. II, nr. 3 (1984), 219-223. L. Zajicek, Porosity and �-porosity, Real Analysis Exchange 13 (1987-88), 314–350. T. Zamfirescu, Porosity in convexity, Real Analysis Exchange 15 (1989-90), 424-436. T. Zamfirescu, Baire categories in convexity, Atti Sem. Mat. Fis. Univ. Modena 39 (1991), no. 1, 139–164. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 36c2a4e7-ac6d-450d-b64c-692a94ff6361 | |
| relation.isAuthorOfPublication.latestForDiscovery | 36c2a4e7-ac6d-450d-b64c-692a94ff6361 |
Download
Original bundle
1 - 1 of 1