On the continuity and differentiability of the (dual) core inverse in C*-algebras

TL;DR

This paper investigates the conditions under which the core inverse and dual core inverse are continuous and differentiable within C*-algebras, including applications to operators and matrices, advancing the understanding of their analytical properties.

Contribution

It provides new results on the continuity and differentiability of the core and dual core inverses in C*-algebras, extending previous work to more general algebraic structures.

Findings

Established conditions for continuity of core and dual core inverses

Analyzed differentiability properties within C*-algebras

Applied results to bounded operators and matrices

Abstract

The continuity of the core inverse and the dual core inverse is studied in the setting of C*-algebras. Later, this study is specialized to the case of bounded Hilbert space operators and to complex matrices. In addition, the differentiability of these generalized inverses is studied in the context of C*-algebras.