Title
Coherent and precoherent operators
Creator
Đikić, Marko S. 1989-
Copyright date
2016
Object Links
Select license
Autorstvo-Nekomercijalno-Bez prerade 3.0 Srbija (CC BY-NC-ND 3.0)
License description
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Language
English
Cobiss-ID
Theses Type
Doktorska disertacija
description
Datum odbrane: 13.12.2016.
Other responsibilities
mentor
Đorđević, Dragan 1970-
član komisije
Rakočević, Vladimir 1953-
član komisije
Pilipovic, Stevan 1950-
član komisije
Živković-Zlatanović, Snežana 1965-
University
Univerzitet u Nišu
Faculty
Prirodno-matematički fakultet
Alternative title
Koherentni i prekoherentni operatori
Publisher
[M. S. Đikić]
Format
[8], IV, 114 listova
description
Biography: list [115]
description
Functional analysis
Abstract (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.
Authors Key words
Koherentni operatori, Prekoherentni operatori, Generalisani
inverzi, Parcijalna uređenja, Paralelna suma, Aditivnost
slika
Authors Key words
Coherent operators, Precoherent operators, Generalized inverses,
Partial orders, Parallel sum, Range additivity
Classification
517.98(043.3)
Subject
517.983.24
Type
Elektronska teza
Abstract (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.
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