Title
Parcijalna uređenja određena uopštenim inverzima i anulatorima : doktorska disertacija
Creator
Rakić, Dragan S. 1983-
Copyright date
2014
Object Links
Select license
Autorstvo-Nekomercijalno-Bez prerade 3.0 Srbija (CC BY-NC-ND 3.0)
License description
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Language
Serbian
Cobiss-ID
Theses Type
PhD thesis
description
Datum odbrane: 05.06.2015.
Other responsibilities
mentor
Đorđević, Dragan S. 1970-
Academic Expertise
Prirodno-matematičke nauke
Academic Title
-
University
Univerzitet u Nišu
Faculty
Prirodno-matematički fakultet
Group
Odsek za matematiku i informatiku
Title translated
Partial orders based on generalized inverses and annihilators
Publisher
NIš : [D. S. Rakić]
Format
PDF/A (178 listova)
description
Umnoženo za odbranu.
Univerzitet u Nišu, Prirodno-matematički fakultet, 2015.
Abstract.
Registar.
Bibliografija: list. 152-158.
Biografija autora: list 1.
description
mathematical analysis
Abstract (en)
The dissertation is a contribution in defining and studying
different types of partial orders on rings, particularly on
von Neumann regular and Rickart rings, as well as on the
algebras of bounded operators on Banach and Hilbert
spaces.
In the first part of the dissertation, using generalized
inverses of elements, the definitions of the minus, star,
sharp, core and dual core partial orders are extended
from the set of complex matrices to an arbitrary ring (with
or without an involution). In a unified approach it is shown
that the condition a<b, where < is one of the above
mentioned relation, or any other G relation, defines two
decompositions of the identity of the ring, and thus, the
representations of a and b in the diagonal 3×3 matrix
forms. It is shown that the most important properties of
the matrix partial orders based on generalized inverses
stay valid in the ring case. Moreover, the considerable
number of new results are proved.
In the second part of the dissertation, the above
mentioned relations are characterized using the notion of
annihilators. This approach allows us to define the
relations for elements which do not possess a generalized
inverse. Partial orders based on annihilators are specially
investigated on the Rickart and Rickart *-rings.
Both approaches give as a corollary the appropriate
results on the algebras of bounded operators on Banach
or Hilbert spaces. The main ideas in the dissertation are
precisely motivated by this case.
Authors Key words
Funkcionalna analiza
Authors Key words
functional analysis
Classification
517
Type
Elektronska teza
Abstract (en)
The dissertation is a contribution in defining and studying
different types of partial orders on rings, particularly on
von Neumann regular and Rickart rings, as well as on the
algebras of bounded operators on Banach and Hilbert
spaces.
In the first part of the dissertation, using generalized
inverses of elements, the definitions of the minus, star,
sharp, core and dual core partial orders are extended
from the set of complex matrices to an arbitrary ring (with
or without an involution). In a unified approach it is shown
that the condition a<b, where < is one of the above
mentioned relation, or any other G relation, defines two
decompositions of the identity of the ring, and thus, the
representations of a and b in the diagonal 3×3 matrix
forms. It is shown that the most important properties of
the matrix partial orders based on generalized inverses
stay valid in the ring case. Moreover, the considerable
number of new results are proved.
In the second part of the dissertation, the above
mentioned relations are characterized using the notion of
annihilators. This approach allows us to define the
relations for elements which do not possess a generalized
inverse. Partial orders based on annihilators are specially
investigated on the Rickart and Rickart *-rings.
Both approaches give as a corollary the appropriate
results on the algebras of bounded operators on Banach
or Hilbert spaces. The main ideas in the dissertation are
precisely motivated by this case.
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