o:1693 Different invertibility modifications in operator spaces and c*-algebras and its applications Modifikacije invertibilnosti na prostorima operatora i c*-algebrama i njihove primene : doctoral dissertation en In this thesis different modifications of invertibility in various settings and their applications are investigated. In particular, the reverse order law is considered for classes of {1,3} and {1,4}-generalized inverses in C*-algebras and particulary in the vector space of linear bounded operators on separable Hilbert spaces. The Hartwig's triple reverse order law for Moore-Penrose inverse is discussed in C*-algebra and ring with involution settings. The reverse order laws on {1,3}, {1,4}, {1,3,4}, {1,2,3} and {1,2,4}-inverses in a ring setting are investigated. This results contain improvements of some known results in C*-algebra case because the assumptions of the regularity of some elements are omitted. The generalized invertibility is applied to solving certain types of equations in rings with unit and determining the general form of solutions. Strictly, the algebraic conditions for the existence of a solution and the expression for the general solution of the system of three linear equations in a ring with a unit are discussed. Another research concerns when the linear combinations of two operators belonging to the class of Fredholm operators. Some cases where the Fredholmness of linear combination is independent of the choice of the scalars are described in detail. Biobibliografija: str. 99-100;Bibliografija: str. 87-97. Datum odbrane: 15.10.2020. Mathematcial analisys, Functional Analysis 28162057 91552101 8093 91552100 28162057 2021-04-27T11:54:07.053Z 45 no 46 mentor Jovana S. 1991- Milošević 2020 63 mentor Dragana 1977- Cvetković Ilić 2020 63 predsednik komisije Vladimir 1953- Rakočević 2020 63 član komisije Vladimir 1976- Pavlović 2020 63 član komisije Jovana 1986- Nikolov-Radenović 2020 [6], 100 str. 1671664 http://phaidrabg.bg.ac.rs/o:1693 no yes 4 2021-04-27T11:54:07.320Z 70 generalized inverses, reverse order law, C*-algebra, ring with involution, Fredholmoperators, systems of linear equations in a ring with a unit uopšteni inverzi, zakon obrnutog redosleda, S*-algebra, prsteni sainvolucijom, Fredholmovi operatori, sistemi linearnih jednačina u prstenu sa jedinicom 517.98(043.3) P140 1738 18A07 18A0701 2020