Submitted:
30 May 2026
Posted:
01 June 2026
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Abstract
In this paper, we establish the coincidence conditions for the generalized core-inverse and (b,c)-inverse of a Banach element. We introduce the generalized core-(b,c)-inverse, a unifying extension characterized via quasinilpotents. A novel limit-based approach is developed to investigate this generalized inverse, yielding polar-like properties and image-based representations that extend the core-(b,c) inverse framework.
Keywords:
generalized core inverse
; (b
; c)-inverse
; polar like property
; Banach algebra
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