A note on Frobenius norm preservers of Jordan product (Q2873575)

Recently, \textit{B.~Kuzma} et al. [Electron. J. Linear Algebra 22, 959--978 (2011; Zbl 1254.15030)] characterized the surjective maps on \(M_n\), \(n\geq 3\), the algebra of \(n\times n\) complex matrices, having the property \(\|\phi(A)\phi(B)+\phi(B)\phi(A)\|=\|AB+BA\|\) for all \(A,B\in M_n\), where \(\|\cdot\|\) denote the Frobenius norm. In the present paper, the surjectivity assumption in relaxed, and a characterization of maps on~\(M_n\), \(n\geq 2\), is given to preserve the above property.