Resumen de A note on the range of generalized derivation

Mohamed Amouch

• Let L(H) denote the algebra of bounded linear operators on a complex separable and infinite dimensional Hilbert space H. For A, B Î L(H), the generalized derivation dA,B associated with (A, B), is defined by dA,B(X) = AX - XB for X Î L(H). In this note we give some sufficient conditions for A and B under which the intersection between the closure of the range of dA,B respect to the given topology and the kernel of dA*,B* vanishes.