Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Chen, Huanyin
Institution: Fuzhou University of International Studies and Trade
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220900112