On the existence of a cyclic vector for some families of operators

• Date: 1993
• Main Authors: Lytvynov, E. V., Литвинов, Є. В.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 1993
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5941
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Under certain restrictions, it is proved that a family of self-adjoint commuting operators $A = (A_{\varphi})_{\varphi \in \Phi}$ where $\Phi$ is a nuclear space, possesses a cyclic vector iff there exists a Hubert space $H \subset \Phi'$ of full operator-valued measure $E$, where $\Phi&am...