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Do some nontrivial closed z-invariant subspaces have the division property ?

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorESTERLE, Jean
dc.date.accessioned2024-04-04T02:54:54Z
dc.date.available2024-04-04T02:54:54Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192316
dc.description.abstractEnWe consider Banach spaces E of functions holomorphic on the open unit disc D such that the unilateral shift S and the backward shift T are bounded on E. Assuming that the spectra of S and T are equal to the closed unit disc we discuss the existence of closed z-invariant of N of E having the "division property", which means that the function f λ : z → f (z)/ z−λ belongs to N for every λ ∈ D and for every f ∈ N such that f (λ) = 0. This question is related to the existence of nontrivial bi-invariant subspaces of Banach spaces of hyperfunctions on the unit circle T.
dc.language.isoen
dc.subject.enAMS Classification : Primary 30B40
dc.subject.en47A15
dc.subject.enSecondary 30B60
dc.subject.en47A68
dc.title.enDo some nontrivial closed z-invariant subspaces have the division property ?
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.subject.halSciences de l'ingénieur [physics]/Autre
dc.subject.halMathématiques [math]/Variables complexes [math.CV]
dc.identifier.arxiv2005.02695
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-02563473
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02563473v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=ESTERLE,%20Jean&rft.genre=preprint


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