Resumen de Linear mapping preserving the kernel or the range of operators
Let X and Y be two in¯nite dimensional real or complex Banach spaces. In this note we determine the forms of surjective additive maps Á : L(X) ! L(Y ) preserving the kernel's dimension or the range's codimension. As consequence, we establish that Á :
L(X) ! L(X) preserves the kernel (respectively, the range) if and only if there exists an invertible operator A 2 L(X) such that Á(T) = AT (respectively, Á(T) = TA) for all T 2 L(X)
