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


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.


Cyclic Vector Nuclear Space Joint Resolution 
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  1. 1.
    V. I. Kolomiets and Yu. S. Samoilenko, “On a countable collection of commuting self-adjoint operators and the algebra of local observables,”Ukr. Mat. Zh.,31, No. 4, 365–371 (1979).Google Scholar
  2. 2.
    A. V. Kosyak and Yu. S. Samoilenko, “On the families of commuting self-adjoint operators,”Ukr. Mat. Zh.,31, No. 5, 555–558 (1979).Google Scholar
  3. 3.
    Yu. S. Samoilenko,Spectral Theory of the Collections of Commuting Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1984).Google Scholar
  4. 4.
    R. L. Dobrushin and R. A. Minlos, “Polynomials of a generalized random field and its moments,”Teor. Veroyatn. Primen.,23, No. 4, 715–729 (1978).Google Scholar
  5. 5.
    Yu. M. Berezanskii and Yu. G. Kondrat'ev,Spectral Methods in Infinite-Dimensional Analysis [in Russian], Naukova Dumka, Kiev (1988).Google Scholar
  6. 6.
    Yu. M. Berezanskii and S. N. Shifrin, “Generalized power symmetric moment problem,”Ukr. Mat. Zh.,23, No. 3, 291–306 (1971).Google Scholar
  7. 7.
    I. M. Gel'fand and N. Ya. Vilenkin,Some Applications of Harmonic Analysis. Rigged Hilbert Spaces [in Russian], Fizmatgiz, Moscow (1961).Google Scholar

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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