Article
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Generalized EP elements in Banach *-algebras
and
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Version 1
: Received: 6 October 2023 / Approved: 6 October 2023 / Online: 9 October 2023 (08:09:37 CEST)
How to cite: Chen, H.; Sheibani, M. Generalized EP elements in Banach *-algebras. Preprints 2023, 2023100393. https://doi.org/10.20944/preprints202310.0393.v1 Chen, H.; Sheibani, M. Generalized EP elements in Banach *-algebras. Preprints 2023, 2023100393. https://doi.org/10.20944/preprints202310.0393.v1
Abstract
We introduce a new generalized inverse (i.e., generalized EP element) which is a natural generalization of EP and *-DMP elements in a Banach *-algebra. We present polar-like characterizations of generalized EP elements. The necessary and sufficient conditions under which the sum of two generalized EP elements is a generalized EP element are investigated. Finally, the generalized core-EP orders for generalized EP elements are characterized.
Keywords
EP element; *-DMP element; generalized core-EP inverse; additive property; generalized core-EP order; 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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