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

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 $A$.

کلیدواژه ها:

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