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Frequent hypercyclicity, chaos, and unconditional Schauder decompositions

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Frequent hypercyclicity, chaos, and unconditional Schauder decompositions

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dc.contributor.author De la Rosa Penilla, Manuel es_ES
dc.contributor.author Frerick, Leonhard es_ES
dc.contributor.author Grivaux, Sophie es_ES
dc.contributor.author Peris Manguillot, Alfredo
dc.date.accessioned 2014-10-27T13:47:09Z
dc.date.available 2014-10-27T13:47:09Z
dc.date.issued 2012-08
dc.identifier.issn 0021-2172
dc.identifier.uri http://hdl.handle.net/10251/43598
dc.description.abstract We prove that if X is any complex separable infinite-dimensional Banach space with an unconditional Schauder decomposition, X supports an operator T which is chaotic and frequently hypercyclic. This result is extended to complex Frechet spaces with a continuous norm and an unconditional Schauder decomposition, and also to complex Frechet spaces with an unconditional basis, which gives a partial positive answer to a problem posed by Bonet. We also solve a problem of Bes and Chan in the negative by presenting hypercyclic, but non-chaotic operators on \mathbb{C}^\mathbb{N}. We extend the main result to C_0-semigroups of operators. Finally, in contrast with the complex case, we observe that there are real Banach spaces with an unconditional basis which support no chaotic operator. es_ES
dc.description.sponsorship This work was partially supported by ANR-Projet Blanc DYNOP, by the MEC and FEDER Projects MTM2007-64222 and MTM2010-14909, and by Generalitat Valenciana Project PROMETEO/2008/101. en_EN
dc.language Inglés es_ES
dc.publisher Springer Verlag (Germany) es_ES
dc.relation ANR-Projet Blanc DYNOP es_ES
dc.relation Ministerio de Educación y Ciencia y FEDER [MTM2007-64222 y MTM2010-14909] es_ES
dc.relation Generalitat Valenciana [PROMETEO/2008/101] es_ES
dc.relation.ispartof Israel Journal of Mathematics es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Fréchet spaces es_ES
dc.subject Schauder decompositions es_ES
dc.subject Banach spaces es_ES
dc.subject Frequently hypercyclic operators es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Frequent hypercyclicity, chaos, and unconditional Schauder decompositions es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s11856-011-0210-6
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.contributor.affiliation Universitat Politècnica de València. Instituto Universitario de Matemática Pura y Aplicada - Institut Universitari de Matemàtica Pura i Aplicada es_ES
dc.description.bibliographicCitation De La Rosa Penilla, M.; Frerick, L.; Grivaux, S.; Peris Manguillot, A. (2012). Frequent hypercyclicity, chaos, and unconditional Schauder decompositions. Israel Journal of Mathematics. 190(1):389-399. doi:10.1007/s11856-011-0210-6 es_ES
dc.description.accrualMethod Senia es_ES
dc.relation.publisherversion http://dx.doi.org/10.1007/s11856-011-0210-6 es_ES
dc.description.upvformatpinicio 389 es_ES
dc.description.upvformatpfin 399 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 190 es_ES
dc.description.issue 1 es_ES
dc.relation.senia 224077
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