When are the products of normal operators normal?

dc.citation.epage150en_US
dc.citation.issueNumber2en_US
dc.citation.spage129en_US
dc.citation.volumeNumber52en_US
dc.contributor.authorGheondea, A.en_US
dc.date.accessioned2016-02-08T10:01:13Z
dc.date.available2016-02-08T10:01:13Z
dc.date.issued2009en_US
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractGiven two normal operators A and B on a Hilbert space it is known that, in general, AB is not normal. The question on characterizing those pairs of normal operators for which their products are normal has been solved for finite dimensional spaces by F.R. Gantmaher and M. G. Krein in 1930, and for compact normal operators by N.A. Wiegmann in 1949. Actually, in the afore mentioned cases, the normality of AB is equivalent with that of BA, and a more general result of F. Kittaneh implies that it is sufficient that AB be normal and compact to obtain that BA is the same. On the other hand, I. Kaplansky had shown that it may be possible that AB is normal while BA is not. When no compactness assumption is made, but both of AB and BA are supposed to be normal, the Gantmaher-KreinWiegmann Theorem can be extended by means of the spectral theory of normal operators in the von Neumann's direct integral representation.en_US
dc.identifier.issn1220-3874
dc.identifier.urihttp://hdl.handle.net/11693/22522
dc.language.isoEnglishen_US
dc.source.titleBulletin Mathematique de la Societe des Sciences Mathematiques de Roumanieen_US
dc.subjectCompact operatoren_US
dc.subjectDecomposable operatoren_US
dc.subjectDirect integral hilbert spaceen_US
dc.subjectNormal operatoren_US
dc.subjectProducten_US
dc.subjectSingular numbersen_US
dc.titleWhen are the products of normal operators normal?en_US
dc.typeArticleen_US

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