A pointwise spectrum and representation of operators

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dc.contributor.authorBertoglio, N
dc.contributor.authorMartinez, S
dc.contributor.authorSan Martin, J
dc.date.accessioned2024-01-10T13:46:00Z
dc.date.available2024-01-10T13:46:00Z
dc.date.issued1998
dc.description.abstractFor a self-adjoint operator A : H --> H commuting with an increasing family of projections P = (P-t) we study the multifunction t --> Gamma(T) (t) = boolean AND {sigma(I) : I an open set of the topology T containing t}, where sigma(I) is the spectrum of A on PIH, Let m(p) be the measure of maximal spectral type. We study the condition that Gamma(T) is essentially a singleton, m(p){t : Gamma(T) (t) is not a singleton} = 0. We show that if T is the density topology and if m(p) satisfies the density theorem, in particular if it is absolutely continuous with respect to the Lebesgue measure, then this condition is equivalent to the fact that A is a Borel function of P. If T is the usual topology then the condition is equivalent to the fact that A is approached in norm by step functions Sigma(n epsilon N) Gamma(T) (alpha(n)) [P(In)f, f], where the set of intervals {I-n : n epsilon N} covers the set where Gamma(T) is a singleton.
dc.fechaingreso.objetodigital2024-04-30
dc.format.extent8 páginas
dc.fuente.origenWOS
dc.identifier.doi10.1090/S0002-9939-98-04428-1
dc.identifier.issn0002-9939
dc.identifier.urihttps://doi.org/10.1090/S0002-9939-98-04428-1
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/79107
dc.identifier.wosidWOS:000071976900008
dc.information.autorucMatemática;Bertoglio A;S/I;49895
dc.issue.numero2
dc.language.isoen
dc.nota.accesocontenido parcial
dc.pagina.final382
dc.pagina.inicio375
dc.publisherAMER MATHEMATICAL SOC
dc.revistaPROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
dc.rightsacceso restringido
dc.titleA pointwise spectrum and representation of operators
dc.typeartículo
dc.volumen126
sipa.codpersvinculados49895
sipa.indexWOS
sipa.indexScopus
sipa.trazabilidadCarga SIPA;09-01-2024
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