Geodesic
Essentially left and right generalized Drazin invertible operators and generalized Saphar decomposition
Filomat, Tome 37 (2023) no. 28, p. 9511

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DOI

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.
DOI : 10.2298/FIL2328511D
Classification : 47A53, 47A10
Keywords: Banach space, operators pencils, left and right Fredholm operators, left and right Weyl operators, left and right generalized Drazin invertible operators, generalized Saphar decomposition, spectrum 
Mirjana D Dimitrijević; Snežana Č Živković-Zlatanović. Essentially left and right generalized Drazin invertible operators and generalized Saphar decomposition. Filomat, Tome 37 (2023) no. 28, p. 9511 . doi: 10.2298/FIL2328511D
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     title = {Essentially left and right generalized {Drazin} invertible operators and generalized {Saphar} decomposition},
     journal = {Filomat},
     pages = {9511 },
     year = {2023},
     volume = {37},
     number = {28},
     doi = {10.2298/FIL2328511D},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2328511D/}
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