Note on the Covariance Coset of the Moore-Penrose Inverses in C-Algebras

Abstract

We will introduce and study several algebraic properties of  the covariance cosets inC algebras. Indeed, we will characterize the covariance coset in terms of commutators. Also, we will show that for an invertible element b, the covariance coset of b−1 coincides with the covariance coset of b . Moreover, if b is normal, then the covariance coset ofb coincides with the covariance coset of b In addition, we will prove that the covariance coset is a cone