Abstract:

For A E/:(H) ( the algebra of all operators on the complex Hilbert space H)~ let 5A
denote the operator on/~(H) defined by : (~A(X) = AX - XA.
We show here that for all Jordan operators A : R(SA) N {A*)' = {0}, where R(6A) is
the range of 6A and (A*}; is the commntant of the adjoint of A.