Linear homeomorphisms of non-classical Hilbert spaces

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dc.contributor.authorSchikhof, WH
dc.contributor.authorOchsenius, H
dc.date.accessioned2024-01-10T13:49:59Z
dc.date.available2024-01-10T13:49:59Z
dc.date.issued1999
dc.description.abstractLet K be a complete infinite rank valued field, In [4] we studied Norm Hilbert Spaces (NHS) over K i.e, K-Banach spaces for which closed subspaces admit projections of norm less than or equal to 1. In this paper we prove the following striking properties of continuous linear operators on NHS. Surjective endomorphisms ale bijective, no NHS is linearly homeomorphic to a proper subspace (Theorem 3.7), each operator can be approximated, uniformly on bounded sets, by finite rank operators (Theorem 3.8). These properties together - in real or complex theory shared only by finite-dimensional spaces - show that NHS are more 'rigid' than classical Hilbert spaces.
dc.fechaingreso.objetodigital16-04-2024
dc.format.extent13 páginas
dc.fuente.origenWOS
dc.identifier.doi10.1016/S0019-3577(00)87912-4
dc.identifier.issn0019-3577
dc.identifier.urihttps://doi.org/10.1016/S0019-3577(00)87912-4
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/79496
dc.identifier.wosidWOS:000084826600013
dc.information.autorucMatemática;Ochsenius M;S/I;315
dc.issue.numero4
dc.language.isoen
dc.nota.accesoContenido parcial
dc.pagina.final613
dc.pagina.inicio601
dc.publisherELSEVIER SCIENCE BV
dc.revistaINDAGATIONES MATHEMATICAE-NEW SERIES
dc.rightsacceso restringido
dc.subject.ods04 Quality Education
dc.subject.odspa04 Educación y calidad
dc.titleLinear homeomorphisms of non-classical Hilbert spaces
dc.typeartículo
dc.volumen10
sipa.codpersvinculados315
sipa.indexWOS
sipa.indexScopus
sipa.trazabilidadCarga SIPA;09-01-2024
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