2017
Том 69
№ 9

Всі номери

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

Литвинов Є. В.

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Абстракт

It is proved that, under some restrictions, a family of selfadjoint commuting operators $A = (A_{\varphi})_{\varphi \in \Phi}$ where $\Phi$ is a nuclear space, has a cyclic vcctor iff there exists a Hilbert space $H \subset \Phi'$ of full operator-valued measure $E$, where $\Phi'$ is the dual of $\Phi$, $E$ is the joint resolution of the identity of the family $A$.

Англомовна версія (Springer): Ukrainian Mathematical Journal 45 (1993), no. 10, pp 1528-1538.

Зразок цитування: Литвинов Є. В. On the existence of a cyclic vector of some families of operators // Укр. мат. журн. - 1993. - 45, № 10. - С. 1362–1370.

Повний текст