Some fixed points preserver

Abstract

Let B(X) and M (F) n be the algebra of all bounded linear operators on a complex Banach<br />space X with dimX 3 and the algebra of all n n matrices over a field F with char F  2 ,<br />respectively. Also let F(A) be the space of all fixed points of an operator AB(X) . In this<br />paper, we characterize the forms of linear maps  :B(X)B(X) which satisfy<br />F(A) = 0F( (A)) = 0 and linear maps :M (F) M (F) n n   which preserve the fixed<br />points of matrices