New properties of weighted generalized core-EP inverse in Banach algebras
Huanyin Chen, Marjan Sheibani
TL;DR
This paper introduces new properties and characterizations of the weighted generalized core-EP inverse in Banach algebras, expanding understanding of its structure and relationships with other inverses.
Contribution
It provides a canonical decomposition, polar-like characterization, and representations of the weighted core-EP inverse using the weighted generalized Drazin inverse, which are novel contributions.
Findings
New properties for the weighted core-EP inverse
Canonical decomposition of the inverse
Representation via weighted generalized Drazin inverse
Abstract
We characterize the generalized weighted core-EP inverse via the canonical decomposition, utilizing a weighted core-EP invertible element and a quasinilpotent. We then offer a polar-like characterization for the generalized weighted core-EP invertible element. The representations of the generalized weighted core-EP inverse by leveraging the weighted generalized Drazin inverse are thereby presented. These lead to new properties for the weighted core-EP inverse.
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Taxonomy
TopicsMatrix Theory and Algorithms · Algebraic and Geometric Analysis · Polynomial and algebraic computation