# Linear maps and covariance sets

Document Type : Research Paper

Author

Institute for Advanced Studies in Basic Sciences(IASBS)

Abstract

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 $C^{\ast}$-Jordan
homomorphisms -under mild assumptions- preserving covariance set and covariance coset in $C^{\ast}$-algebras.

Keywords