o:1421
Kato type decompositions and generalizations of Drazin invertibility
Dekompozicije Katoovog tipa i uopštenja Drazinove invertibilnosti : doctoral dissertation
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.
Biography: str. [91] Datum odbrane: 11.10.2017. Functional analysis
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no
46
mentor
Miloš D. 1983-
Cvetković
2017
63
mentor
Snežana 1965-
Živković-Zlatanović
2017
63
član komisije
Vladimir 1953-
Rakočević
2017
63
član komisije
Dragan 1970-
Đorđević
2017
63
član komisije
Stevan 1950-
Pilipovic
2017
63
član komisije
Dijana 1981-
Mosić
2017
VI, 90 str.
4665008
http://phaidrabg.bg.ac.rs/o:1421
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Katoova dekompozicija, Katoov operator, semi-Fredholmovioperatori, uopšteni Drazinov spektar, operatorske matrice,Banahova algebra, zatvoren operator
Kato decomposition, Kato operator, semi-Fredholm operators,generalized Drazin spectrum, operator matrices, Banach algebra,closed operator
517.983.23:517.984.3(043.3)
P 140
1738
18A07
18A0701
2017