Kato type decompositions and generalizations of Drazin invertibility
Докторанд
Cvetković, Miloš D.Ментор
Živković-Zlatanović, SnežanaЧланови комисије
Rakočević, VladimirĐorđević, Dragan
Pilipovic, Stevan
Mosić, Dijana
Метаподаци
Приказ свих података о дисертацијиСажетак
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 alg...ebra
element. These objects are characterized and their main properties are
studied. We also extend some results from the Fredholm theory to
unbounded closed operators.