Nonlinear invertibility preserving maps on matrix algebras

摘要

Let M-n denote the algebra of all n x n matrices over the complex field C. We prove that if the maps phi, psi : M-n ->( )M(n )have the property that for every x, y is an element of M-n and lambda is an element of C we have that lambda x + y is an element of M-n is invertible if and only if lambda phi (x) + psi (y) is an element of M-n is invertible, and one of the maps (,c, or is either surjective or continuous, there exist then invertible matrices u, upsilon is an element of M-n such that either