Integral Equations and Operator Theory

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dc.contributor.authorBiswas, Animikh
dc.contributor.authorPetrovic, Srdjan
dc.date.accessioned2024-11-14T15:18:16Z
dc.date.available2024-11-14T15:18:16Z
dc.date.issued2005-12-20
dc.description.abstractA complex number λ is an extended eigenvalue of an operator A if there is a nonzero operator X such that AX  =  λXA. We characterize the set of extended eigenvalues, which we call extended point spectrum, for operators acting on finite dimensional spaces, finite rank operators, Jordan blocks, and C₀ contractions. We also describe the relationship between the extended eigenvalues of an operator A and its powers. As an application, we show that the commutant of an operator A coincides with that of Aⁿ, n ≥ 2, n ∈ N if the extended point spectrum of A does not contain any n–th root of unity other than 1. The converse is also true if either A or A* has trivial kernel.
dc.description.sponsorshipThe first author was partially supported by NSF grant number DMS – 0074460 and by the Junior Summer Research Fellowship (2003) from University of North Carolina at Charlotte. The second author was supported in part by the FRACASF grant from the Western Michigan University.
dc.description.urihttps://link.springer.com/article/10.1007/s00020-005-1381-5
dc.format.extent15 pages
dc.genrejournal articles
dc.genrepreprints
dc.identifierdoi:10.13016/m2vm4i-o5se
dc.identifier.citationBiswas, Animikh, and Srdjan Petrovic. “Integral Equations and Operator Theory.” Integral Equations and Operator Theory 55, no. 2 (June 1, 2006): 233–48. https://doi.org/10.1007/s00020-005-1381-5.
dc.identifier.urihttps://doi.org/10.1007/s00020-005-1381-5
dc.identifier.urihttp://hdl.handle.net/11603/36896
dc.language.isoen_US
dc.publisherSpringer
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mathematics and Statistics Department
dc.rightsThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
dc.subject47B15
dc.subject47B38
dc.subject47B49
dc.subjectC0 contraction
dc.subjectExtended eigenvalues
dc.subjectPrimary 47A65
dc.subjectSecondary 47A62
dc.titleIntegral Equations and Operator Theory
dc.title.alternativeOn extended eigenvalues of operators
dc.typeText
dcterms.creatorhttps://orcid.org/0000-0001-8594-0568

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