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

  • E. V. Lytvynov

Abstract

Under certain restrictions, it is proved that a family of self-adjoint commuting operators A=(Aφ)φΦ where Φ is a nuclear space, possesses a cyclic vector iff there exists a Hubert space HΦ 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.
Published
25.10.1993
How to Cite
Lytvynov, E. 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.
Section
Research articles