%0 Journal Article
%T On Preserving Properties of Linear Maps on $C^{*}$-algebras
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Golfarshchi, Fatemeh
%A Khalilzadeh, Ali Asghar
%D 2020
%\ 01/01/2020
%V 17
%N 1
%P 125-137
%! On Preserving Properties of Linear Maps on $C^{*}$-algebras
%K Absolute value preserving
%K $*$-homomorphism
%K Unitary preserving
%K numerical range
%R 10.22130/scma.2019.107553.607
%X Let $A$ 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.
%U https://scma.maragheh.ac.ir/article_37336_c7070f356e0ff49cbe395cf74a73eedd.pdf