Linear Maps Preserving Invertibility or Spectral Radius on Some $C^{*}$-algebras

Abstract

Let $A$ be a unital $C^{*}$-algebra which has a faithful state. If $varphi:Arightarrow A$ is a unital linear map which is bijective and invertibility preserving or surjective and spectral radius preserving, then $varphi$ is a Jordan isomorphism. Also, we discuss other types of linear preserver maps on $A$.

Keywords

• $C^{*}$-algebra
• Hilbert $C^{*}$-module
• Invertibility preserving
• Spectral radius preserving
• Jordan isomorphism