On the existence of a cyclic vector for some families of operators
Abstract
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 $\Phi'$ is the space dual to $\Phi$, $E$ is the joint resolution of the identity of the family $A$.
Published
25.10.1993
How to Cite
LytvynovE. V. “On the Existence of a Cyclic Vector for Some Families of Operators”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 45, no. 10, Oct. 1993, pp. 1362–1370, https://umj.imath.kiev.ua/index.php/umj/article/view/5941.
Issue
Section
Research articles