Maps preserving trace of products of matrices

Huajun Huang, Ming-Cheng Tsai

We prove the linearity and injectivity of two maps ${\varphi }_1$ and ${\varphi }_2$ on certain subsets of $M_n$ that satisfy $\mathrm{tr}({\varphi }_1(A){\varphi }_2(B))=\mathrm{tr}(AB)$. We apply it to…