DETERMINANT AND SPECTRUM PRESERVING MAPS ON M_n

Abstract

Abstract. Let M n be the algebra of all complex n × n matrices and ϕ : M n → M n a surjective map (not necessarily additive or multiplicative) satisfying one of the following equations:Then it is an automorphism, where σ(A) is the spectrum of A ∈ M n . We also show that if A be a standard operator algebra, B is a unital Banach algebra with trivial center and if ϕ : A → B is a multiplicative surjection preserving spectrum, then ϕ is an algebra isomorphism.