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

• Published in: Український математичний журнал
• Date: 1993
• Main Author: Lytvynov, E. V.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 1993
• Subjects: Статті
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/155297
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On the existence of a cyclic vector of some families of operators / E. V. Lytvynov // Український математичний журнал. — 1993. — Т. 45, № 10. — С. 1362–1370.. — Бібліогр.: 7 назв. — англ.

It is proved that, under some restrictions, a family of selfadjoint commuting operators A=(Aφ) φ ∈ Φ where Φ is a nuclear space, has a cyclic vcctor iff there exists a Hilbert space H ⊂ Φ′ of full operator-valued measure E, where Φ′ is the dual of Φ, E is the joint resolution of the identity of the...