GD1 inverse and 1GD inverse for bounded operators on Banach spaces

Sahoo, JK and Boggarapu, P and Behera, R and Nashed, MZ (2023) GD1 inverse and 1GD inverse for bounded operators on Banach spaces. In: Computational and Applied Mathematics, 42 (5).

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Abstract

Mosić and Djordjević introduced the notation of the gDMP inverse for a linear operator on Hilbert space in Mosić and Djordjević (J Spectr Theory 8(2):555–573, 2018) by considering generalized Drazin inverse with the Moore-Penrose inverse. This article introduces two new classes of inverses: GD1 (generalized Drazin and inner) inverse and 1GD (inner and generalized Drazin) inverse for Banach space operators. The existence and uniqueness of the GD1 (also 1GD) inverse are discussed along with some properties through core-quasinilpotent decomposition and closed range decomposition operator. We further establish a few explicit representations of the GD1 inverse and their interconnections with generalized Drazin inverse. In addition, we discuss a few properties of GD1 (also 1GD) inverse through binary relation.

Item Type:	Journal Article
Publication:	Computational and Applied Mathematics
Publisher:	Springer Nature
Additional Information:	The copyright for this article belongs to Springer Nature.
Keywords:	Banach space operators; Drazin inverse; GDMP inverse; Generalized Drazin inverse; Inner inverse.
Department/Centre:	Division of Interdisciplinary Sciences > Computational and Data Sciences
Date Deposited:	18 Jul 2023 09:39
Last Modified:	18 Jul 2023 09:39
URI:	https://eprints.iisc.ac.in/id/eprint/82456

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