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Weighted Generalized Group Inverse in Banach *-Algebras
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Version 1
: Received: 3 October 2023 / Approved: 4 October 2023 / Online: 4 October 2023 (07:21:50 CEST)
How to cite: Chen, H.; Sheibani, M. Weighted Generalized Group Inverse in Banach *-Algebras. Preprints 2023, 2023100219. https://doi.org/10.20944/preprints202310.0219.v1 Chen, H.; Sheibani, M. Weighted Generalized Group Inverse in Banach *-Algebras. Preprints 2023, 2023100219. https://doi.org/10.20944/preprints202310.0219.v1
Abstract
In this paper, we introduce the notion of weighted generalized group inverse in a Banach algebra with proper involution. This is a natural generalization of weighted weak group inverse for a complex matrix and Hilbert space operator. We present several characterizations and representations of this generalized inverse. In addition, a new partial order on elements in a Banach *-algebra is investigated by using the weighted generalized group inverse and some known results are thus generalized.
Keywords
generalized core-EP inverse; generalized group inverse; weighted generalized Drazin inverse; weighted weak group inverse; Banach *-algebra
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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