Title
Kato type decompositions and generalizations of Drazin invertibility
Creator
Cvetković, Miloš D. 1983-
Copyright date
2017
Object Links
Select license
Autorstvo-Nekomercijalno-Bez prerade 3.0 Srbija (CC BY-NC-ND 3.0)
License description
Dozvoljavate samo preuzimanje i distribuciju dela, ako/dok se pravilno naznačava ime autora, bez ikakvih promena dela i bez prava komercijalnog korišćenja dela. Ova licenca je najstroža CC licenca. Osnovni opis Licence: http://creativecommons.org/licenses/by-nc-nd/3.0/rs/deed.sr_LATN. Sadržaj ugovora u celini: http://creativecommons.org/licenses/by-nc-nd/3.0/rs/legalcode.sr-Latn
Language
English
Cobiss-ID
Theses Type
Doktorska disertacija
description
Datum odbrane: 11.10.2017.
Other responsibilities
mentor
Živković-Zlatanović, Snežana 1965-
član komisije
Rakočević, Vladimir 1953-
član komisije
Đorđević, Dragan 1970-
član komisije
Pilipovic, Stevan 1950-
član komisije
Mosić, Dijana 1981-
Academic Expertise
Prirodno-matematičke nauke
Academic Title
-
University
Univerzitet u Nišu
Faculty
Prirodno-matematički fakultet
Group
Odsek za matematiku i informatiku
Alternative title
Dekompozicije Katoovog tipa i uopštenja Drazinove invertibilnosti
Publisher
[M. D. Cvetković]
Format
VI, 90 str.
description
Biography: str. [91]
description
Functional analysis
Abstract (en)
The main objective of this dissertation is to give necessary and
sufficient conditions under which a bounded linear operator T can be
represented as the direct sum of a nilpotent (quasinilpotent, Riesz)
operator TN and an operator TM which belongs to any of the
following classes: upper (lower) semi-Fredholm operators, Fredholm
operators, upper (lower) semi-Weyl operators, Weyl operators, upper
(lower) semi-Browder operators, Browder operators, bounded below
operators, surjective operators and invertible operators. These results
are applied to different types of spectra. In addition, we introduce the
notions of the generalized Kato-Riesz decomposition and generalized
Drazin-Riesz invertible operators.
Moreover, we study the generalized Drazin spectrum of an upper
triangular operator matrix acting on the product of Banach or
separable Hilbert spaces.
Further, motivated by the Atkinson type theorem for B-Fredholm
operators, we introduce the notion of a B-Fredholm Banach algebra
element. These objects are characterized and their main properties are
studied. We also extend some results from the Fredholm theory to
unbounded closed operators.
Authors Key words
Katoova dekompozicija, Katoov operator, semi-Fredholmovi
operatori, uopšteni Drazinov spektar, operatorske matrice,
Banahova algebra, zatvoren operator
Authors Key words
Kato decomposition, Kato operator, semi-Fredholm operators,
generalized Drazin spectrum, operator matrices, Banach algebra,
closed operator
Classification
517.983.23:517.984.3(043.3)
Subject
P 140
Type
Elektronska teza
Abstract (en)
The main objective of this dissertation is to give necessary and
sufficient conditions under which a bounded linear operator T can be
represented as the direct sum of a nilpotent (quasinilpotent, Riesz)
operator TN and an operator TM which belongs to any of the
following classes: upper (lower) semi-Fredholm operators, Fredholm
operators, upper (lower) semi-Weyl operators, Weyl operators, upper
(lower) semi-Browder operators, Browder operators, bounded below
operators, surjective operators and invertible operators. These results
are applied to different types of spectra. In addition, we introduce the
notions of the generalized Kato-Riesz decomposition and generalized
Drazin-Riesz invertible operators.
Moreover, we study the generalized Drazin spectrum of an upper
triangular operator matrix acting on the product of Banach or
separable Hilbert spaces.
Further, motivated by the Atkinson type theorem for B-Fredholm
operators, we introduce the notion of a B-Fredholm Banach algebra
element. These objects are characterized and their main properties are
studied. We also extend some results from the Fredholm theory to
unbounded closed operators.
“Data exchange” service offers individual users metadata transfer in several different formats. Citation formats are offered for transfers in texts as for the transfer into internet pages. Citation formats include permanent links that guarantee access to cited sources. For use are commonly structured metadata schemes : Dublin Core xml and ETUB-MS xml, local adaptation of international ETD-MS scheme intended for use in academic documents.