Mostrar el registro sencillo del ítem

Sin título

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorESTERLE, Jean
dc.date.accessioned2024-04-04T02:23:11Z
dc.date.available2024-04-04T02:23:11Z
dc.date.created2012-02-15
dc.date.issued2012-06-01
dc.identifier.issn2008-8752
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189712
dc.description.abstractEnI. Kaplansky showed in 1947 that every submultiplicative norm ∥.∥ on the algebra C(K) of complex-valued functions on an infinite compact space K satisfies ∥f∥ ≥ ∥f∥_K for every f ∈ C(K), where ∥f∥_K = maxt∈K|f(t)| denotes the standard norm on C(K). He asked whether all submultiplicative norms ∥.∥ were in fact equivalent to the standard norm (which is obviously true for finite compact spaces), or equivalently, whether all homomorphisms from C(K) into a Banach algebra were continuous. This problem turned out to be undecidable in ZFC, and we will discuss here some recent progress due to Pham and open questions concerning the structure of the set of nonmaximal prime ideals of C(K) which are closed with respect to a discontinuous sub- multiplicative norm on C(K) when the continuum hypothesis is assumed. We will also discuss the existence of discontinuous characters on Fr ́echet algebras (Michael's problem), a long standing problem which remains unsolved. The Mittag-Leffler theorem on inverse limits of complete metric spaces plays an essential role in the literature concerning both problems.
dc.language.isoen
dc.publisherMashhad : Tusi Mathematical Research Group
dc.subject.enautomatic continuity
dc.subject.encontinuity of characters
dc.subject.enFréchet algebra
dc.subject.enMittag-Leffler theorem
dc.subject.enKaplansky's problem
dc.typeArticle de revue
dc.identifier.doi10.15352/afa/1399899933
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
bordeaux.journalAnnals of Functional Analysis
bordeaux.page66-88
bordeaux.volume3
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue2
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00773372
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00773372v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Annals%20of%20Functional%20Analysis&rft.date=2012-06-01&rft.volume=3&rft.issue=2&rft.spage=66-88&rft.epage=66-88&rft.eissn=2008-8752&rft.issn=2008-8752&rft.au=ESTERLE,%20Jean&rft.genre=article


Archivos en el ítem

ArchivosTamañoFormatoVer

No hay archivos asociados a este ítem.

Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro sencillo del ítem