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The Szlenk index and the fixed point property under renorming


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dc.creator Domínguez Benavides, Tomás es 2016-09-27T10:12:21Z 2016-09-27T10:12:21Z 2010
dc.identifier.citation Domínguez Benavides, T. (2010). The Szlenk index and the fixed point property under renorming. Fixed Point Theory and Applications, 2010, 1-9.
dc.identifier.issn 1687-1820 es
dc.identifier.issn 1687-1812 es
dc.description.abstract Assume that X is a Banach space such that its Szlenk index Sz X is less than or equal to the first infinite ordinal ω. We prove that X can be renormed in such a way that X with the resultant norm satisfies R X < 2, where R · is the García-Falset coefficient. This leads us to prove that if X is a Banach space which can be continuously embedded in a Banach space Y with Sz Y ≤ ω, then, X can be renormed to satisfy the w-FPP. This result can be applied to Banach spaces which can be embedded in C K , where K is a scattered compact topological space such that K ω ∅. Furthermore, for a Banach space X, ·, we consider a distance in the space P of all norms in X which are equivalent to · for which P becomes a Baire space. If Sz X ≤ ω, we show that for almost all norms in the sense of porosity in P, X satisfies the w-FPP. For general reflexive spaces independently of the Szlenk index, we prove another strong generic result in the sense of Baire category. es
dc.description.sponsorship Dirección General de Enseñanza Superior es
dc.description.sponsorship Junta de Andalucía es
dc.format application/pdf es
dc.language.iso eng es
dc.publisher Springer Open es
dc.relation.ispartof Fixed Point Theory and Applications, 2010, 1-9.
dc.rights Attribution-NonCommercial-NoDerivatives 4.0 Internacional *
dc.rights.uri *
dc.title The Szlenk index and the fixed point property under renorming es
dc.type info:eu-repo/semantics/article es
dc.type.version info:eu-repo/semantics/publishedVersion es
dc.rights.accessrights info:eu-repo/semantics/openAccess es
dc.contributor.affiliation Universidad de Sevilla. Departamento de Análisis Matemático es
dc.relation.projectID BFM2006-13997-C02-01 es
dc.relation.projectID FQM-127 es
dc.relation.publisherversion es
dc.identifier.doi 10.1155/2010/268270 es Universidad de Sevilla. FQM127: Análisis Funcional no Lineal es
idus.format.extent 9 p. es
dc.journaltitle Fixed Point Theory and Applications es
dc.publication.volumen 2010 es
dc.publication.initialPage 1 es
dc.publication.endPage 9 es
dc.contributor.funder Dirección General de Enseñanza Superior. España
dc.contributor.funder Junta de Andalucía
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