Title
Perturbacije uopštenih inverza elemenata u prstenima
Creator
Mihajlović, Nadica 1973
CONOR:
109063177
Copyright date
2023
Object Links
Language
Serbian
CobissID
Theses Type
Doktorska disertacija
description
Datum odbrane: 22. 08. 2023.
Other responsibilities
Academic Expertise
Prirodnomatematičke nauke
Academic Title

University
Univerzitet u Nišu
Faculty
Prirodnomatematički fakultet
Group
Odsek za matematiku i informatiku
Alternative title
Perturbations of generalised inverses of the elements in rings
Publisher
[N. M. Mihajlović]
Format
[5], 107 listova
description
Bibliografija: listovi 100107
description
Theory of operators; functional analysis
Abstract (en)
The topic of this doctoral dissertation is the study of some perturbation properties of generalized inverses of the elements in rings with or without involution, as well as in Banach algebra and C*algebra. So far, the problems are mostly investigated in the case of the matrices, i.e. operators on finite dimensional vector spaces. The idea was to use decompositions of elements in rings induced by idempotents, instead of matrix decompositions. In this way, the calculus in rings approaches to the calculus in the set of 2x2 matrices over mentioned ring. The additional difficulty appears in using idempotents in Banach and C*algebras. Starting from the matrix form of an arbitrary ring element regarding to a corresponding idempotents, the matrix forms of the group and core inverse with respect to the same idempotents are constructed. Several characterizations are established for the forward order law for the MoorePenrose inverse to hold. The results valid for matrices have been extended to elements of arbitrary Banach algebras. Further, we introduced the acute perturbation for the group inverse in Banach algebra with the respect to the spectral radius instead of the spectral the norm. In this way, we described an explicit expression that connects the group inverses of the initial and the perturbed elements. Moreover, more simple expressions for the perturbation of the generalized inverses are obtained and the optimal perturbation bounds for the core inverse presented when the perturbation satisfies certain conditions.
Authors Key words
grupni inverz, MurPenrouzov inverz, jezgarni inverz, prsten sa involucijom, Banahova algebra, C*algebra, perturbacije, zakon nepromenjenog redosleda
Authors Key words
group inverse, MoorePenrose inverse, core inverse, ring with involution, Banach algebra, C*algebra, perturbations, forward order law
Classification
517.983/.986(043.3)
Subject
P140
Type
Tekst
Abstract (en)
The topic of this doctoral dissertation is the study of some perturbation properties of generalized inverses of the elements in rings with or without involution, as well as in Banach algebra and C*algebra. So far, the problems are mostly investigated in the case of the matrices, i.e. operators on finite dimensional vector spaces. The idea was to use decompositions of elements in rings induced by idempotents, instead of matrix decompositions. In this way, the calculus in rings approaches to the calculus in the set of 2x2 matrices over mentioned ring. The additional difficulty appears in using idempotents in Banach and C*algebras. Starting from the matrix form of an arbitrary ring element regarding to a corresponding idempotents, the matrix forms of the group and core inverse with respect to the same idempotents are constructed. Several characterizations are established for the forward order law for the MoorePenrose inverse to hold. The results valid for matrices have been extended to elements of arbitrary Banach algebras. Further, we introduced the acute perturbation for the group inverse in Banach algebra with the respect to the spectral radius instead of the spectral the norm. In this way, we described an explicit expression that connects the group inverses of the initial and the perturbed elements. Moreover, more simple expressions for the perturbation of the generalized inverses are obtained and the optimal perturbation bounds for the core inverse presented when the perturbation satisfies certain conditions.
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