- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 Mapping preserving numerical range of operator products on ${C}^*$-algebras Bull. Korean Math. Soc. 2015 Vol. 52, No. 6, 1963-1971 https://doi.org/10.4134/BKMS.2015.52.6.1963Published online November 30, 2015 Mohamed Mabrouk Faculty of Sciences Abstract : Let $\ala$ and $\alb$ be two unital $C^*$-algebras. Denote by $W(a)$ the numerical range of an element $a\in\ala$. We show that the condition $W(ax)=W(bx), \forall x\in\ala$ implies that $a=b$. Using this, among other results, it is proved that if $\phi: \ala\rightarrow\alb$ is a surjective map such that $W(\phi(a)\phi(b)\phi(c)) = W(abc)$ for all $a, b$ and $c \in\ala$, then $\phi(1)\in Z(B)$ and the map $\psi=\phi(1)^2\phi$ is multiplicative. Keywords : $C^*$-algebras, numerical range, preserving the numerical range MSC numbers : 15A86, 46L05, 47A12, 47B49 Full-Text :