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Cvetković, Miloš D. 1983
Kato type decompositions and generalizations of Drazin invertibility
AutorstvoNekomercijalnoBez prerade 3.0 Srbija (CC BYNCND 3.0)
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Academic metadata
Doktorska disertacija
Prirodnomatematičke nauke

Univerzitet u Nišu
Prirodnomatematički fakultet
Odsek za matematiku i informatiku
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Dekompozicije Katoovog tipa i uopštenja Drazinove invertibilnosti
[M. D. Cvetković]
VI, 90 str.
Biography: str. [91]
Datum odbrane: 11.10.2017.
Functional analysis
ŽivkovićZlatanović, Snežana 1965 (mentor)
Rakočević, Vladimir 1953 (član komisije)
Đorđević, Dragan 1970 (član komisije)
Pilipovic, Stevan 1950 (član komisije)
Mosić, Dijana 1981 (član komisije)
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) semiFredholm operators, Fredholm
operators, upper (lower) semiWeyl operators, Weyl operators, upper
(lower) semiBrowder 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 KatoRiesz decomposition and generalized
DrazinRiesz 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 BFredholm
operators, we introduce the notion of a BFredholm 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.
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) semiFredholm operators, Fredholm
operators, upper (lower) semiWeyl operators, Weyl operators, upper
(lower) semiBrowder 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 KatoRiesz decomposition and generalized
DrazinRiesz 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 BFredholm
operators, we introduce the notion of a BFredholm 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.