On the existence of a cyclic vector for some families of operators
Under certain restrictions, it is proved that a family of self-adjoint commuting operatorsA=(Aϕ)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.
KeywordsCyclic Vector Nuclear Space Joint Resolution
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