- -

Convergence of arithmetic means of operators in Fréchet spaces

RiuNet: Institutional repository of the Polithecnic University of Valencia

Share/Send to

Cited by

Statistics

  • Estadisticas de Uso

Convergence of arithmetic means of operators in Fréchet spaces

Show simple item record

Files in this item

dc.contributor.author Albanese, Angela Ama es_ES
dc.contributor.author Bonet Solves, José Antonio es_ES
dc.contributor.author Ricker, Werner J. es_ES
dc.date.accessioned 2014-10-08T12:19:54Z
dc.date.available 2014-10-08T12:19:54Z
dc.date.issued 2013-05-01
dc.identifier.issn 0022-247X
dc.identifier.uri http://hdl.handle.net/10251/43075
dc.description.abstract Every Köthe echelon Fréchet space XX that is Montel and not isomorphic to a countable product of copies of the scalar field admits a power bounded continuous linear operator TT such that I−TI−T does not have closed range, but the sequence of arithmetic means of the iterates of TT converges to 0 uniformly on the bounded sets in XX. On the other hand, if XX is a Fréchet space which does not have a quotient isomorphic to a nuclear Köthe echelon space with a continuous norm, then the sequence of arithmetic means of the iterates of any continuous linear operator TT (for which (1/n)Tn(1/n)Tn converges to 0 on the bounded sets) converges uniformly on the bounded subsets of XX, i.e., TT is uniformly mean ergodic, if and only if the range of I−TI−T is closed. This result extends a theorem due to Lin for such operators on Banach spaces. The connection of Browder’s equality for power bounded operators on Fréchet spaces to their uniform mean ergodicity is exposed. An analysis of the mean ergodic properties of the classical Cesàro operator on Banach sequence spaces is also given. © 2012 Elsevier Ltd. All rights reserved. es_ES
dc.description.sponsorship The research of Jose Bonet was partially supported by MEC and FEDER Project MTM 2007-62643, GV Project Prometeo/2008/101 (Spain) and ACOMP/2012/090. en_EN
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation.ispartof Journal of Mathematical Analysis and Applications es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Fréchet space es_ES
dc.subject Köthe echelon space es_ES
dc.subject Power bounded operator es_ES
dc.subject Prequojection es_ES
dc.subject Quojection es_ES
dc.subject Uniformly mean ergodic operator es_ES
dc.subject Equation es_ES
dc.subject Spectrum es_ES
dc.subject Banach-Spaces es_ES
dc.subject Uniform ergodic theorem es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Convergence of arithmetic means of operators in Fréchet spaces es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1016/j.jmaa.2012.11.060
dc.relation.projectID info:eu-repo/grantAgreement/MEC//MTM2007-62643/ES/METODOS DE ANALISIS FUNCIONAL PARA EL ANALISIS COMPLEJO Y LAS ECUACIONES EN DERIVADAS PARCIALES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEO08%2F2008%2F101/ES/Análisis funcional, teoría de operadores y aplicaciones/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//ACOMP%2F2012%2F090/ 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 Albanese, AA.; Bonet Solves, JA.; Ricker, WJ. (2013). Convergence of arithmetic means of operators in Fréchet spaces. Journal of Mathematical Analysis and Applications. 401(1):160-173. https://doi.org/10.1016/j.jmaa.2012.11.060 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://dx.doi.org/10.1016/j.jmaa.2012.11.060 es_ES
dc.description.upvformatpinicio 160 es_ES
dc.description.upvformatpfin 173 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 401 es_ES
dc.description.issue 1 es_ES
dc.relation.senia 235795
dc.identifier.eissn 1096-0813
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Ministerio de Educación y Ciencia es_ES


This item appears in the following Collection(s)

Show simple item record