Abstract:

In this paper, we give some structure features of the multiplicative maps and the rank preserving multiplicative maps on matrix algebra M_n(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.

Key words: Multiplicative maps, Rank, Spectral radius, Normal matrices