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Ukrainian Mathematical Journal

, Volume 45, Issue 10, pp 1528–1538 | Cite as

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

  • E. V. Lytvynov
Article

Abstract

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.

Keywords

Cyclic Vector Nuclear Space Joint Resolution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • E. V. Lytvynov
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

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