On the existence of a cyclic vector for some families of operators - Lytvynov, E. V. (Ukrains’kyi Matematychnyi Zhurnal, 1993)
Under certain restrictions, it is proved that a family of self-adjoint commuting operators A = (A_φ)_φ Φ where Φ is a nuclear space, possesses a cyclic vector iff there exists a Hubert space H Φ’ of full operator-valued measure E, where Φ’ is the space dual to Φ, E is the joint resolution of the identity of the family A.