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Normal functionals on Lipschitz spaces are weak* continuous

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Normal functionals on Lipschitz spaces are weak* continuous

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dc.contributor.author Aliaga, Ramón J. es_ES
dc.contributor.author Pernecká, Eva es_ES
dc.date.accessioned 2023-12-05T19:03:46Z
dc.date.available 2023-12-05T19:03:46Z
dc.date.issued 2022-11 es_ES
dc.identifier.issn 1474-7480 es_ES
dc.identifier.uri http://hdl.handle.net/10251/200529
dc.description.abstract [EN] Let Lip0(M) be the space of Lipschitz functions on a complete metric space M that vanish at a base point. We prove that every normal functional in Lip0(M)¿ is weak* continuous; that is, in order to verify weak* continuity it suffices to do so for bounded monotone nets of Lipschitz functions. This solves a problem posed by N. Weaver. As an auxiliary result, we show that the series decomposition developed by N. J. Kalton for functionals in the predual of Lip0(M) can be partially extended to Lip0(M)¿. es_ES
dc.description.sponsorship The authors thank Michal Doucha and Richard J. Smith for their helpful comments and the anonymous reviewers for their nice suggestions. R. J. Aliaga was partially supported by the Spanish Ministry of Economy, Industry and Competitiveness under Grant MTM2017-83262-C2-2-P. E. Perneck ' a was supported by Grant GA.CR 18-00960Y from the Czech Science Foundation. es_ES
dc.language Inglés es_ES
dc.publisher Cambridge University Press es_ES
dc.relation.ispartof Journal of the Institute of Mathematics of Jussieu es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Lipschitz-free space es_ES
dc.subject Lipschitz function es_ES
dc.subject Lipschitz space es_ES
dc.subject Normal functional es_ES
dc.subject.classification TECNOLOGIA ELECTRONICA es_ES
dc.title Normal functionals on Lipschitz spaces are weak* continuous es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1017/S147474802100013X es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-83262-C2-2-P/ES/LA INTERACCION ENTRE GEOMETRIA Y TOPOLOGIA EN ESPACIOS DE BANACH. APLICACIONES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GACR//GACR 18-00960Y/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Escuela Técnica Superior de Ingenieros de Telecomunicación - Escola Tècnica Superior d'Enginyers de Telecomunicació es_ES
dc.description.bibliographicCitation Aliaga, RJ.; Pernecká, E. (2022). Normal functionals on Lipschitz spaces are weak* continuous. Journal of the Institute of Mathematics of Jussieu. 21(6):2093-2102. https://doi.org/10.1017/S147474802100013X es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1017/S147474802100013X es_ES
dc.description.upvformatpinicio 2093 es_ES
dc.description.upvformatpfin 2102 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 21 es_ES
dc.description.issue 6 es_ES
dc.relation.pasarela S\478628 es_ES
dc.contributor.funder Grant Agency of the Czech Republic es_ES
dc.contributor.funder Ministerio de Economía, Industria y Competitividad es_ES


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