%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 $a,b\in A$, then $\varphi$ is a $*$-homomorphism. It is also shown that if $\varphi(|ab|)=|\varphi(a)\varphi(b)|$ for all $a,b\in A$, then $\varphi$ is a unital $*$-homomorphism.
%U https://scma.maragheh.ac.ir/article_37336_5e75596460a797fec56dbf1fd1ff1242.pdf