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 $A = (A_{φ})_{φ \in Φ}$ where $Φ$ is a nuclear space, possesses a cyclic vector iff there exists a Hubert space $H \subset Φ'$ 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 $A$.