University of MaraghehSahand Communications in Mathematical Analysis2322-580717120200101On Preserving Properties of Linear Maps on $C^{*}$-algebras1251373733610.22130/scma.2019.107553.607ENFatemehGolfarshchiDepartment of Multimedia, Tabriz
Islamic Art University, Tabriz, Iran.Ali AsgharKhalilzadehDepartment of Mathematics, Sahand University of Technology, Sahand Street, Tabriz, Iran.Journal Article20190508Let $A$ and $B$ be two unital $C^{*}$-algebras and $varphi:A rightarrow B$ be a linear map. In this paper, we investigate the structure of linear maps between two $C^{*}$-algebras that preserve a certain property or relation. In particular, we show that if $varphi$ is unital, $B$ is commutative and $V(varphi(a)^{*}varphi(b))subseteq V(a^{*}b)$ for all $a,bin A$, then $varphi$ is a $*$-homomorphism. It is also shown that if $varphi(|ab|)=|varphi(a)varphi(b)|$ for all $a,bin A$, then $varphi$ is a unital $*$-homomorphism.https://scma.maragheh.ac.ir/article_37336_c7070f356e0ff49cbe395cf74a73eedd.pdf