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Envelopes in Banach spaces

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dc.contributor.authorFerenczi, Valentin
dc.contributor.authorLópez Abad, Jorge
dc.contributor.orcidhttps://orcid.org/0000-0001-5239-111X
dc.date.accessioned2025-02-11T12:50:35Z
dc.date.available2025-02-11T12:50:35Z
dc.date.issued2024-07-12
dc.descriptionThe registered version of this article, first published in “Banach Journal of Mathematical Analysis, 18(3), paper No. 59", is available online at the publisher's website: Springer, https://orcid.org/0000-0001-5239-111X
dc.descriptionLa versión registrada de este artículo, publicado por primera vez en “Banach Journal of Mathematical Analysis, 18(3), paper No. 59", está disponible en línea en el sitio web del editor: Springer, https://orcid.org/0000-0001-5239-111X
dc.description.abstractWe introduce the notion of isometric envelope of a subspace in a Banach space, establishing its connections with several key elements: (a) we explore its relation to the mean ergodic projection on fixed points within a semigroup of contractions, (b) we draw parallels with Korovkin sets from the 1970s, (c) we investigate its impact on the extension properties of linear isometric embeddings. We use this concept to address the recent conjecture that the Gurarij space and the spaces Lp, p∉2N+4 are the only separable approximately ultrahomogeneous Banach spaces (a certain multidimensional transitivity of the action of the linear isometry group). The similar conjecture for Fraïssé Banach spaces (a strengthening of the approximately homogeneous property) is also considered. We characterize the Hilbert space as the only separable reflexive space in which any closed subspace coincides with its envelope; and we show that the Gurarij space satisfies the same property. We compute some envelopes in the case of Lebesgue spaces, showing that the reflexive Lp-spaces are the only reflexive rearrangement invariant spaces on [0, 1] for which all 1-complemented subspaces are envelopes. We also identify the isometrically unique “full” quotient space of Lp by a Hilbertian subspace, for appropriate values of p, as well as the associated topological group embedding of the unitary group into the isometry group of Lp.en
dc.description.versionversión publicada
dc.identifier.citationFerenczi, & Lopez-Abad. (2024). Envelopes in Banach spaces. Banach Journal of Mathematical Analysis, 18(3). https://doi.org/10.1007/S43037-024-00346-W
dc.identifier.doihttps://doi.org/10.1007/s43037-024-00346-w
dc.identifier.issn2662-2033 | eISSN 1735-8787
dc.identifier.urihttps://hdl.handle.net/20.500.14468/25897
dc.journal.issue3
dc.journal.titleBanach Journal of Mathematical Analysis
dc.journal.volume18
dc.language.isoes
dc.publisherSpringer
dc.relation.centerFacultades y escuelas::Facultad de Ciencias
dc.relation.departmentMatemáticas Fundamentales
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/deed.es
dc.subject12 Matemáticas
dc.titleEnvelopes in Banach spaceses
dc.typeartículoes
dc.typejournal articleen
dspace.entity.typePublication
relation.isAuthorOfPublicationaaddef9e-5f78-4f63-ac00-1bc271b3e71f
relation.isAuthorOfPublication.latestForDiscoveryaaddef9e-5f78-4f63-ac00-1bc271b3e71f
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