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dc.contributor.author | Guirao Sánchez, Antonio José![]() |
es_ES |
dc.contributor.author | Montesinos Santalucia, Vicente![]() |
es_ES |
dc.contributor.author | Zizler, Vaclav![]() |
es_ES |
dc.date.accessioned | 2018-03-26T07:04:48Z | |
dc.date.available | 2018-03-26T07:04:48Z | |
dc.date.issued | 2015 | es_ES |
dc.identifier.issn | 0002-9939 | es_ES |
dc.identifier.uri | http://hdl.handle.net/10251/99757 | |
dc.description.abstract | [EN] Morris (1983) proved that every separable Banach space $X$ that contains an isomorphic copy of $c_0$ has an equivalent strictly convex norm such that all points of its unit sphere $S_X$ are unpreserved extreme, i.e., they are no longer extreme points of $B_{X^{**}}$. We use a result of Hájek (1995) to prove that any separable infinite-dimensional polyhedral Banach space has an equivalent $C^{\infty}$-smooth and strictly convex norm with the same property as in Morris' result. We additionally show that no point on the sphere of a $C^2$-smooth equivalent norm on a polyhedral infinite-dimensional space can be strongly extreme, i.e., there is no point $ x$ on the sphere for which a sequence $ (h_n)$ in $ X$ with $ \Vert h_n\Vert\not \to 0$ exists such that $ \Vert x\pm h_n\Vert\to 1$. | es_ES |
dc.description.sponsorship | The first author’s research was supported by Ministerio de Econom´ıa y Competitividad and FEDER under project MTM2011-25377 and the Universitat Polit`ecnica de Val`encia. The second author’s research was supported by Ministerio de Econom´ıa y Competitividad and FEDER under project MTM2011-22417 and the Universitat Polit`ecnica de Val`encia | |
dc.language | Inglés | es_ES |
dc.publisher | American Mathematical Society | es_ES |
dc.relation.ispartof | Proceedings of the American Mathematical Society | es_ES |
dc.rights | Reserva de todos los derechos | es_ES |
dc.subject | Polyhedral space | es_ES |
dc.subject | Extreme point | es_ES |
dc.subject | Norm that locally depends on a finite number of coordinates | es_ES |
dc.subject | Countable James boundary | es_ES |
dc.subject.classification | MATEMATICA APLICADA | es_ES |
dc.title | A note on extreme points of $C^\infty$-smooth balls in polyhedral spaces | es_ES |
dc.type | Artículo | es_ES |
dc.identifier.doi | 10.1090/S0002-9939-2015-12617-2 | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/MICINN//MTM2011-25377/ES/LA INTERACCION ENTRE TEORIA DE LA MEDIDA, TOPOLOGIA Y ANALISIS FUNCIONAL./ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/MICINN//MTM2011-22417/ES/ESPACIOS Y ALGEBRAS DE FUNCIONES DIFERENCIABLES/ | es_ES |
dc.rights.accessRights | Abierto | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada | es_ES |
dc.description.bibliographicCitation | Guirao Sánchez, AJ.; Montesinos Santalucia, V.; Zizler, V. (2015). A note on extreme points of $C^\infty$-smooth balls in polyhedral spaces. Proceedings of the American Mathematical Society. 143(8):3413-3420. https://doi.org/10.1090/S0002-9939-2015-12617-2 | es_ES |
dc.description.accrualMethod | S | es_ES |
dc.relation.publisherversion | http://dx.doi.org/10.1090/S0002-9939-2015-12617-2 | es_ES |
dc.description.upvformatpinicio | 3413 | es_ES |
dc.description.upvformatpfin | 3420 | es_ES |
dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.description.volume | 143 | es_ES |
dc.description.issue | 8 | es_ES |
dc.relation.pasarela | S\284590 | es_ES |
dc.contributor.funder | Ministerio de Ciencia e Innovación | es_ES |