Norm Hilbert spaces over Krull valued fields

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dc.contributor.authorOchsenius, H.
dc.contributor.authorSchikhof, W. H.
dc.date.accessioned2024-01-10T12:40:57Z
dc.date.available2024-01-10T12:40:57Z
dc.date.issued2006
dc.description.abstractNorm Hilbert spaces (NHS) are defined as Banach spaces over valued fields (see 1.4) for which each closed subspace has a norm-orthogonal complement. For fields with a rank I valuation, these spaces were characterized already in [10, 5.13, 5.16], where it was proved that infinite-dimensional NHS exist only if the valuation of K is discrete. The first discussion of the case of (Krull) valued fields appeared in [1] and [3]. In this paper we continue and expand this work focussing on the most interesting cases, not covered before. If K is not metrizable then each NHS is finite-dimensional (Corollary 3.2.2), but otherwise there do exist infinite-dimensional NHS; they are completely described in 3.2.5. Our main result is Theorem 3.2.1, where various characterizations of NI-IS of different nature are presented. Typical results are that NHS arc of countable type, that they have orthogonal bases, and that no subspace is linearly homeomorphic to co.
dc.fechaingreso.objetodigital17-04-2024
dc.format.extent20 páginas
dc.fuente.origenWOS
dc.identifier.doi10.1016/S0019-3577(06)80007-8
dc.identifier.eissn1872-6100
dc.identifier.issn0019-3577
dc.identifier.urihttps://doi.org/10.1016/S0019-3577(06)80007-8
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/77366
dc.identifier.wosidWOS:000237521900006
dc.information.autorucMatemática;Ochsenius M;S/I;315
dc.issue.numero1
dc.language.isoen
dc.nota.accesoContenido parcial
dc.pagina.final84
dc.pagina.inicio65
dc.publisherELSEVIER SCIENCE BV
dc.revistaINDAGATIONES MATHEMATICAE-NEW SERIES
dc.rightsacceso restringido
dc.subjectLipschitz operators
dc.subjectHilbert spaces
dc.subjectKrull valued fields
dc.subject.ods04 Quality Education
dc.subject.odspa04 Educación y calidad
dc.titleNorm Hilbert spaces over Krull valued fields
dc.typeartículo
dc.volumen17
sipa.codpersvinculados315
sipa.indexWOS
sipa.indexScopus
sipa.trazabilidadCarga SIPA;09-01-2024
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