2019
Том 71
№ 11

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

Lytvynov E. V.

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 $A$.

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

Citation Example: Lytvynov E. V. On the existence of a cyclic vector for some families of operators // Ukr. Mat. Zh. - 1993. - 45, № 10. - pp. 1362–1370.

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