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arXiv · 2610.06866

Generalized [v,w]-core inverse in Banach *-algebras

Huanyin Chen
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Abstract

We introduce the generalized weighted core inverse with respect to two elements in a Banach *-algebra, extending the framework of existing generalized inverses. This new generalized inverse is characterized via the generalized weighted core decomposition, and its representations are established using the weighted g-Drazin inverse. We investigate the polar-like and principal ideal properties to reveal its structural behavior. Consequently, applications to complex matrices are derived. This finds encompasses both the core-EP and generalized core inverses, significantly broadening the theoretical framework.

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Huanyin Chen. 2026-08-12. Generalized [v,w]-core inverse in Banach *-algebras. https://arxiv.org/abs/2610.06866

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