Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Weighted Generalized Group Inverse in Banach *-Algebras

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

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.

Leave a public comment
Send a private comment to the author(s)
* All users must log in before leaving a comment
Views 0
Downloads 0
Comments 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.