On denseness of certain norms in Banach spaces
| dc.contributor.author | Jiménez Sevilla, María Del Mar | |
| dc.contributor.author | Moreno, José Pedro | |
| dc.date.accessioned | 2023-06-20T18:49:43Z | |
| dc.date.available | 2023-06-20T18:49:43Z | |
| dc.date.issued | 1996 | |
| dc.description.abstract | We give several results dealing with denseness of certain classes of norms with many vertex points. We prove that, in Banach spaces with the Mazur or the weak* Mazur intersection property, every ball (convex body) can be uniformly approximated by balls (convex bodies) being the closed convex hull of their strongly vertex points. We also prove that given a countable set F, every norm can be uniformly approximated by norms which are locally linear at each point of F. | |
| 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/22698 | |
| dc.identifier.issn | 0004-9727 | |
| dc.identifier.officialurl | http://0-journals.cambridge.org.cisne.sim.ucm.es/action/displayAbstract?fromPage=online&aid=4787532&fulltextType=RA&fileId=S0004972700017640 | |
| dc.identifier.relatedurl | http://0-journals.cambridge.org.cisne.sim.ucm.es/action/login?sessionId=8879B93727AC1AB44D1A4D6F56BEADCB.journals | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/58716 | |
| dc.issue.number | 2 | |
| dc.journal.title | Bulletin of the Australian Mathematical Society | |
| dc.language.iso | eng | |
| dc.page.final | 196 | |
| dc.page.initial | 183 | |
| dc.publisher | Cambridge University Press | |
| dc.relation.projectID | PB 93-0452 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 514.7 | |
| dc.subject.ucm | Geometría diferencial | |
| dc.subject.unesco | 1204.04 Geometría Diferencial | |
| dc.title | On denseness of certain norms in Banach spaces | |
| dc.type | journal article | |
| dc.volume.number | 54 | |
| dcterms.references | Deville, R., Godefroy, G. and Zizler, V., Smoothness and renormings in Banach spaces, Monograph Surveys Pure Appl. Math. 64 (Pitman, 1993). Fabian, M., ‘Lipschitz smooth points of convex functions and isomorphic characterizations of Hilbert spaces’, Proc. London Math. Soc. 51 (1985), 113–126. Fonf, V., ‘Three characterizations of polyhedral Banach spaces’, Ukrain. Math. J. 42 (1990), 1145–1148. Georgiev, P.G., ‘Fréchet differentiability of convex functions in separable Banach spaces’, C.R. Acad. Bulgare. Sci. 43 (1990), 13–15. Georgiev, P.G., ‘On the residuality of the set of norms having Mazur's intersection property’, Math. Balkanica 5 (1991), 20–26. Giles, J.R., Gregory, D.A. and Sims, B., ‘Characterization of normed linear spaces with Mazur's intersection property’, Bull. Austral. Math. Soc. 18 (1978), 471–476. Godun, B.V. and Troyanski, S.L., ‘Renorming Banach spaces with fundamental biorthogonal system’, Contemp. Math. 144 (1993), 119–126. Sevilla, M. Jiménez and Moreno, J.P., ‘The Mazur intersection property and Asplund spaces’, C.R. Acad. Sci. Paris Séric. I Math. 321 (1995), 1219–1223. Sevilla, M. Jiménez and Moreno, J.P., ‘Renorming Banach spaces with the Mazur intersection property’, J. Funct. Anal, (to appear). Kunen, K. and Vaugham, J., Handbook of set theoretic topology (North Holland, 1984). Mazur, S., ‘Über schwache Konvergentz in den Raumen Lp’, Studia Math. 4 (1933), 128–133. Moreno, J.P., ‘Geometry of Banach spaces with (α, ε)-property or (β,ε)-property’, Rocky Mountain J. Math, (to appear). Moreno, J.P., ‘On the weak* Mazur intersection property and Fréchet differentiable norms on dense open sets’, Bull. Sci. Math. (to appear). Schachermayer, W., ‘Norm attaining operators and renormings of Banach spaces’, Israel J. Math. 44 (1983), 201–212. Shelah, S., ‘Uncountable constructions for B. A., e. c. and Banach spaces’, Israel J. Math. 51 (1985), 273–297. Vanderwerff, J., ‘Fréchet differentiable norms on spaces of countable dimension’, Arch. Math. 58 (1992), 471–476. | |
| 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