Document Type : Research Paper

Author

• Mohammad Hossein Alizadeh ^{1, 2}

¹ Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran

² Department of Mathematics, Islamic Azad University, Nur Branch, Nur, Iran

Abstract

Let $\mathcal{A}$ and $\mathcal{B}$\ are $C^{\ast }$-algebras. A linear map $\varphi :\mathcal{A}\to \mathcal{B}$ 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

• Moore-Penrose inverse
• covariance set
• Jordan homomorphism