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Ukrainian Mathematical Journal

, Volume 49, Issue 6, pp 984–987 | Cite as

A remark on quasianalytic vectors for a pair of anticommuting operators

  • S. V. Tishchenko
Brief Communications
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Abstract

We prove that two self-adjoint operators that anticommute on the dense invariant domain of their common quasianalytic vectors are strongly anticommuting.

Keywords

Hilbert Space Naukova Dumka Weak Convergence Strong Convergence Strong Sense 
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

  1. 1.
    E. Nelson, “Analytic vectors,” Ann. Math., 70, No. 3, 572–615 (1959).CrossRefGoogle Scholar
  2. 2.
    A. E. Nussbaum, “Quasi-analytic vectors,” Ark. Mat., 6, No. 2, 179–191 (1965).zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    F. H. Vasilescu, “Anticommuting selfadjoint operators,” Rev. Roum. Math. Pures Appl., 28, 77–91 (1983).zbMATHMathSciNetGoogle Scholar
  4. 4.
    Yu. S. Samoilenko, Spectral Theory for Collections of Self-Adjoint Operators. [in Russian], Naukova Dumka, Kiev (1984).Google Scholar
  5. 5.
    S. Pedersen, “Anticommuting selfadjoint operators,” J. Funct. Anal., 89, No. 2, 428–443 (1990).zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    M. H. Stone, Linear Transformations in Hilbert Space, AMS, New York (1932).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • S. V. Tishchenko

There are no affiliations available

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