ALGEBRAIC DEGREE IN SPATIAL MATRICIAL NUMERICAL RANGES OF LINEAR OPERATORS

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dc.contributor.authorBernik, Janez
dc.contributor.authorLivshits, Leo
dc.contributor.authorMacDonald, Gordon W.
dc.contributor.authorMarcoux, Laurent W.
dc.contributor.authorMastnak, Mitja
dc.contributor.authorRadjavi, Heydar
dc.date.accessioned2022-05-10T18:51:22Z
dc.date.available2022-05-10T18:51:22Z
dc.date.issued2021-07-20
dc.descriptionFirst published in Proceedings of the American Mathematical Society in volume 149, issue 10 in 2021, published by the American Mathematical Societyen
dc.description.abstractWe study the maximal algebraic degree of principal ortho-compressions of linear operators that constitute spatial matricial numerical ranges of higher order. We demonstrate (amongst other things) that for a (possibly unbounded) operator L on a Hilbert space, every principal m-dimensional ortho-compression of L has algebraic degree less than m if and only if rank(L − λI) ≤ m − 2 for some λ ∈ Cen
dc.description.sponsorshipThe first author’s research was supported in part by Research and Development Agency of Slovenia grant P1-0222. The second author’s research was supported by Colby College Natural Sciences Division Grant. The third, fourth, and fifth authors’ research was supported in part by NSERC (Canada).en
dc.identifier.urihttps://doi.org/10.1090/proc/15523
dc.identifier.urihttp://hdl.handle.net/10012/18251
dc.language.isoenen
dc.publisherAmerican Mathematical Societyen
dc.subjectspatial matricial numerical rangesen
dc.subjectalgebraic degreeen
dc.subjectrank modulo scalarsen
dc.subjectorthogonal compressionsen
dc.subjectprincipal submatricesen
dc.subjectcyclic matricesen
dc.subjectnon-derogatory matricesen
dc.titleALGEBRAIC DEGREE IN SPATIAL MATRICIAL NUMERICAL RANGES OF LINEAR OPERATORSen
dc.typeArticleen
dcterms.bibliographicCitationBernik, J., Livshits, L., MacDonald G. W., Marcoux L. W., Mastnak, M., Radjavi, H. (2021, July 20). Algebraic degree in spatial matricial numerical ranges of linear operators. Proceedings of the American Mathematical Society, 149(10), 4083-4097. https://doi.org/10.1090/proc/15523en
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2Pure Mathematicsen
uws.peerReviewStatusRevieweden
uws.scholarLevelFacultyen
uws.typeOfResourceTexten

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