@article {
author = {Golfarshchi, Fatemeh and Khalilzadeh, Ali Asghar},
title = {On Preserving Properties of Linear Maps on $C^{*}$-algebras},
journal = {Sahand Communications in Mathematical Analysis},
volume = {17},
number = {1},
pages = {125-137},
year = {2020},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2019.107553.607},
abstract = {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.},
keywords = {Absolute value preserving,$*$-homomorphism,Unitary preserving,numerical range},
url = {https://scma.maragheh.ac.ir/article_37336.html},
eprint = {https://scma.maragheh.ac.ir/article_37336_5e75596460a797fec56dbf1fd1ff1242.pdf}
}