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dc.contributor.advisorŽivković-Zlatanović, Snežana
dc.contributor.otherRakočević, Vladimir
dc.contributor.otherĐorđević, Dragan
dc.contributor.otherPilipovic, Stevan
dc.contributor.otherMosić, Dijana
dc.creatorCvetković, Miloš D.
dc.date.accessioned2017-12-19T09:04:50Z
dc.date.available2017-12-19T09:04:50Z
dc.date.available2020-07-03T16:12:36Z
dc.date.issued2017-10-11
dc.identifier.urihttp://nardus.mpn.gov.rs/handle/123456789/8998
dc.identifier.urihttp://eteze.ni.ac.rs/application/showtheses?thesesId=5455
dc.identifier.urihttps://fedorani.ni.ac.rs/fedora/get/o:1421/bdef:Content/download
dc.identifier.urihttp://vbs.rs/scripts/cobiss?command=DISPLAY&base=70052&RID=1025546985
dc.description.abstractThe main objective of this dissertation is to give necessary and sufficient conditions under which a bounded linear operator T can be represented as the direct sum of a nilpotent (quasinilpotent, Riesz) operator TN and an operator TM which belongs to any of the following classes: upper (lower) semi-Fredholm operators, Fredholm operators, upper (lower) semi-Weyl operators, Weyl operators, upper (lower) semi-Browder operators, Browder operators, bounded below operators, surjective operators and invertible operators. These results are applied to different types of spectra. In addition, we introduce the notions of the generalized Kato-Riesz decomposition and generalized Drazin-Riesz invertible operators. Moreover, we study the generalized Drazin spectrum of an upper triangular operator matrix acting on the product of Banach or separable Hilbert spaces. Further, motivated by the Atkinson type theorem for B-Fredholm operators, we introduce the notion of a B-Fredholm Banach algebra element. These objects are characterized and their main properties are studied. We also extend some results from the Fredholm theory to unbounded closed operators.en
dc.formatapplication/pdf
dc.languageen
dc.publisherУниверзитет у Нишу, Природно-математички факултетsr
dc.rightsopenAccessen
dc.sourceУниверзитет у Нишуsr
dc.subjectKatoova dekompozicijasr
dc.subjectKato decompositionen
dc.subjectKato operatoren
dc.subjectsemi-Fredholm operatorsen
dc.subjectgeneralized Drazin spectrumen
dc.subjectoperator matricesen
dc.subjectBanach algebraen
dc.subjectclosed operatoren
dc.subjectKatoov operatorsr
dc.subjectsemi-Fredholmovi operatorisr
dc.subjectuopšteni Drazinov spektarsr
dc.subjectoperatorske matricesr
dc.subjectBanahova algebrasr
dc.subjectzatvoren operatorsr
dc.titleKato type decompositions and generalizations of Drazin invertibilitysr
dc.typedoctoralThesis
dc.rights.licenseBY-NC-ND
dcterms.abstractЖивковић-Златановић, Снежана; Ракочевић, Владимир; Ђорђевић, Драган; Пилиповиц, Стеван; Мосић, Дијана; Цветковић, Милош Д.;
dc.identifier.fulltexthttp://nardus.mpn.gov.rs/bitstream/id/54424/Cvetkovic_Milos_D.pdf
dc.identifier.fulltexthttp://nardus.mpn.gov.rs/bitstream/id/54423/Disertacija.pdf


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