Generalized weighted group inverse in Banach algebras with proper involution

Huanyin Chen

doi:10.20944/preprints202406.1867.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 26 June 2024 / Approved: 26 June 2024 / Online: 27 June 2024 (08:10:56 CEST)

In this paper, we introduce the notion of the generalized $w$-group inverse in a Banach algebra with proper involution. This is a natural generalization of generalized (weak) group inverse in Banach *-algebras. Many elementary properties of such new weighted generalized inverse are presented. We further establish the equivalent relations between generalized weighted group inverse and weighted generalized Drazin inverse. Related properties of generalized (weak) group inverse are extended to the wider cases.

weighted generalized Drazin inverse; weighted group inverse; weak group inverse; complex matrix; Banach algebra.

Computer Science and Mathematics, Algebra and Number Theory

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Generalized weighted group inverse in Banach algebras with proper involution

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