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

We study several algebraic properties of dual covariance and weighted dual covariance sets in rings with involution and c∗ -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 multiplicativec∗ -functions. © 2014 hesam mahzoon.