Affiliation:
1. Department of Mathematics, University of Niš, Faculty of Sciences and Mathematics, Niš, Serbia
Abstract
In this paper we define and study the classes of the essentially left and
right generalized Drazin invertible operators and of the left and
rightWeyl-g-Drazin invertible operators by means of the analytical core and
the quasinilpotent part of an operator. We show that the essentially left
(right) generalized Drazin invertible operator can be represented as a sum
of a left (right) Fredholm and a quasinilpotent operator. Analogously, the
left (right) Weyl-g-Drazin invertible operator can be represented as a sum
of a left (right) Weyl and a quasinilpotent operator. We also characterize
these operators in terms of their generalized Saphar decompositions,
accumulation and interior points of various spectra of operator pencils.
Furthermore, we expand the results from [10], on the left and right
generalized Drazin invertible operators. Special attention is devoted to the
investigation of the corresponding spectra of operator pencils.
Publisher
National Library of Serbia
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