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Subspaces of $\displaystyle H^{p}$ linearly homeomorphic to $l^{p}.$

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorAMAR, Eric
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorCHEVREAU, Bernard
hal.structure.identifierÉquations aux dérivées partielles, analyse [EDPA]
dc.contributor.authorCHALENDAR, Isabelle
dc.date.accessioned2024-04-04T03:14:24Z
dc.date.available2024-04-04T03:14:24Z
dc.date.created2016-02-11
dc.date.issued2019
dc.identifier.issn0039-3223
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194054
dc.description.abstractEnWe present two fast constructions of weak*-copies of ℓ ∞ in H ∞ and show that such copies are necessarily weak*-complemented. Moreover, via a Paley-Wiener type of stability theorem for bases, a connection can be made in some cases between the two types of construction, via interpolating sequences (in fact these are at the basis of the second construction). Our approach has natural generalizations where H ∞ is replaced by an arbitrary dual space and ℓ ∞ by ℓ p (1 ≤ p ≤ ∞) relying on the notions of generalized interpolating sequence and bounded linear extension. An old (very simple but unpublished so far) construction of bases which are Besselian but not Hilbertian finds a natural place in this development.
dc.language.isoen
dc.publisherInstytut Matematyczny - Polska Akademii Nauk
dc.subject.enBesselian and Hilbertian bases
dc.subject.enH^p spaces
dc.subject.eninterpolating sequences.
dc.title.enSubspaces of $\displaystyle H^{p}$ linearly homeomorphic to $l^{p}.$
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Variables complexes [math.CV]
dc.identifier.arxiv1607.02762
bordeaux.journalStudia Mathematica
bordeaux.pagepp. 233-253.
bordeaux.volume248
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue3
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01343701
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01343701v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Studia%20Mathematica&rft.date=2019&rft.volume=248&rft.issue=3&rft.spage=pp.%20233-253.&rft.epage=pp.%20233-253.&rft.eissn=0039-3223&rft.issn=0039-3223&rft.au=AMAR,%20Eric&CHEVREAU,%20Bernard&CHALENDAR,%20Isabelle&rft.genre=article


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