Linear maps and covariance sets

Let \mathcal{A} and \mathcal{B}\ are C^{{\huge \ast}} -algebras\textbf{.} A\textbf{ }linear map \phi:\mathcal{A\rightarrow B} is C^{\ast}-Jordan homomorphism if it is a Jordan homomorphism which preserves the adjoint operation. In this note we show that C^{\ast}-Jordanhomomorphisms -under mild assumptions- preserving covariance set and covariance coset in C^{\ast}-algebras.

Linear maps and covariance sets Keywords:

Moore-Penrose inverse , covariance set , Jordan homomorphism