Multiplicative trace and spectrum preservers on stochastic matrices

Ming-Cheng Tsai, Huajun Huang

We characterize maps ${\varphi }_i:\mathcal{S}\to \mathcal{S}$, $i=1,\dots ,m$ and $m\ge 1$, that have the multiplicative spectrum or trace preserving property: \begin{eqnarray*} \textr…