We show that the separating subspaces for the component operators of a densely valued homomorphism pair into anH*-triple system are contained in the annihilator ideal. Accordingly, the continuity of densely valued homomorphisms into H^*-algebras and H^*-triple systems with zero annihilator follows.

We investigate the commutation between a continuous linear random operator and a continuous linear deterministic operator on a Banach space. From this we obtain probabilistic versions of theorems by Fuglede and Putnam, both of them dealing with the commutation between continuous linear operators with continuous normal operators on a Hilbert space.