Abstract
Under certain restrictions, it is proved that a family of self-adjoint commuting operatorsA=(A ϕ)ϕεΦ where Φ is a nuclear space, possesses a cyclic vector iff there exists a Hubert spaceH ⊂ Φ′ of full operator-valued measureE, where Φ′ is the space dual to Φ andE is the joint resolution of the identity of the familyA.
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References
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Published in Ukrainskii Matematicheskii Zhurnal, Vol.45, No. 10, pp. 1362–1370, October, 1993.
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Lytvynov, E.V. On the existence of a cyclic vector for some families of operators. Ukr Math J 45, 1528–1538 (1993). https://doi.org/10.1007/BF01571087
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DOI: https://doi.org/10.1007/BF01571087