Modifikacije invertibilnosti na prostorima operatora i c*-algebrama i njihove primene

[J. S. Milošević]

[6], 100 str.

Biobibliografija: str. 99-100; Bibliografija: str. 87-97.

Mathematcial analisys, Functional Analysis

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.

generalized inverses, reverse order law, C*-algebra, ring with involution, Fredholm operators, systems of linear equations in a ring with a unit

uopšteni inverzi, zakon obrnutog redosleda, S*-algebra, prsteni sa involucijom, Fredholmovi operatori, sistemi linearnih jednačina u prstenu sa jedinicom

517.98(043.3)

P140

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