o:1289 Coherent and precoherent operators Koherentni i prekoherentni operatori : doctoral dissertation en In this thesis we introduce and investigate new classes of operators which we call coherent and precoherent operators. These operators appear as solutions of some problems in the literature, but they also represent a generalization of some frequently studied classes of operators. After we study different properties of these new classes, we continue by considering a few interesting problems in operator theory. We consider problems about the Moore-Penrose inverse and arbitrary reflexive inverse of the sum of operators, range additivity of operators, lattice properties of the star and core partial orders on Hilbert space operators, the connection about the parallel sum of operators and their infimum in different partial orders, and one special type of operators, inspired by recently introduced disjoint range operators. Accordingly, we generalize and improve a number of results from the existing literature. One part of the thesis is dedicated to Rickart *-rings and generalizations of some presented results in the algebraic setting. We included a number of examples in order to demonstrate our statements and their possible extent: reduction of conditions, proving opposite directions, etc. In the end, we propose few problems for further research on these topics. Biography: list [115] Datum odbrane: 13.12.2016. Functional analysis 1025419753 91552101 4713 91552100 1025419753 2017-03-27T11:43:25.053Z 45 no 46 mentor Marko S. 1989- Đikić 2016 63 mentor Dragan 1970- Đorđević 2016 63 član komisije Vladimir 1953- Rakočević 2016 63 član komisije Stevan 1950- Pilipovic 2016 63 član komisije Snežana 1965- Živković-Zlatanović 2016 [8], IV, 114 listova 4336535 http://phaidrabg.bg.ac.rs/o:1289 no yes 4 2017-03-27T11:43:25.320Z 70 Koherentni operatori, Prekoherentni operatori, Generalisaniinverzi, Parcijalna uređenja, Paralelna suma, Aditivnostslika Coherent operators, Precoherent operators, Generalized inverses,Partial orders, Parallel sum, Range additivity 517.98(043.3) 517.983.24 1738 18A07 2016