Revista de la
Unión Matemática Argentina
Weighted weak group inverse in a ring with involution
Huanyin Chen

Volume 69, no. 1 (2026), pp. 247–268    

Published online (final version): February 24, 2026

https://doi.org/10.33044/revuma.5074

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Abstract

We introduce the concept of the weighted weak group inverse for elements in a ring with involution. This notion naturally extends the weak group inverse for complex matrices and the weighted weak group inverse for Hilbert operators. We characterize this generalized inverse through a novel decomposition (referred to as the $w$-group decomposition) that involves weighted group inverses and nilpotent elements. Additionally, the interrelationships among weighted weak group inverses, weighted Drazin inverses, and weighted core-EP core inverses are thoroughly investigated.

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