Multiplication-Preserving Maps On Matrix Algebras
矩阵代数上的可乘保持映射

In this paper, we give some structure features of the multiplicative maps and the rank preserving multiplicative maps on matrix algebra Mn(F), where F is a field. By applying these results, we get some characterizations of the multiplicative maps on complex matrix algebras which preserve any one of the spectral radius, numerical radius, numerical range, positivity, self-adjointness, normality and unitarity of matrices.