o:1421 Kato type decompositions and generalizations of Drazin invertibility Dekompozicije Katoovog tipa i uopštenja Drazinove invertibilnosti : doctoral dissertation en The 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. Biography: str. [91] Datum odbrane: 11.10.2017. Functional analysis 1025546985 91552101 5455 91552100 1025546985 2017-12-13T19:27:06.053Z 45 no 46 mentor Miloš D. 1983- Cvetković 2017 63 mentor Snežana 1965- Živković-Zlatanović 2017 63 član komisije Vladimir 1953- Rakočević 2017 63 član komisije Dragan 1970- Đorđević 2017 63 član komisije Stevan 1950- Pilipovic 2017 63 član komisije Dijana 1981- Mosić 2017 VI, 90 str. 4665008 http://phaidrabg.bg.ac.rs/o:1421 no yes 4 2017-12-13T19:27:06.320Z 70 Katoova dekompozicija, Katoov operator, semi-Fredholmovioperatori, uopšteni Drazinov spektar, operatorske matrice,Banahova algebra, zatvoren operator Kato decomposition, Kato operator, semi-Fredholm operators,generalized Drazin spectrum, operator matrices, Banach algebra,closed operator 517.983.23:517.984.3(043.3) P 140 1738 18A07 18A0701 2017