Coherent and precoherent operators
Author
Đikić, Marko S.Mentor
Đorđević, DraganCommittee members
Rakočević, VladimirPilipovic, Stevan

Živković-Zlatanović, Snežana
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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
generaliza...tions 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.