This research introduces the weighted w-core inverse and explores its relations to the ω-core inverse in Banach algebras, suggesting new decompositions.
We introduce the weighted w-core inverse in a Banach algebra and establish its fundamental properties. We examine its connections to the ω-core inverse and explore element associated with the decomposition of the weighted ω-core inverse. This foundation allows for the investigation of a novel generalized inverse formed by integrating the core and w-group inverse.
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Huanyin Chen (2025) studied this question.
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