Weighted Dual Covariance Moore-Penrose Inverses with respect to an Invertible Element in C*-Algebras

Abstract

We study several algebraic properties of dual covariance and weighted dual covariance sets in rings with involution and $C^{\mathrm{*}}$-algebras. Moreover, we show that the weighted dual covariance set, seen as a multivalued map, has some kind of continuity. Also, we prove weighed dual covariance set invariant under the bijection multiplicative $\mathrm{*}$-functions.