Ukrainian Mathematical Journal

, Volume 46, Issue 7, pp 962–970 | Cite as

Essential normality of some classes of operators in tensor products of Hilbert spaces

  • V. O. Livinskii


We establish general criteria for the domains of definition of spectral integrals to be essential. On the basis of these criteria, we prove that some classes of operators are essentially normal in tensor products of Hilbert spaces.


Hilbert Space Tensor Product General Criterion Spectral Integral Essential Normality 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. A. Naimark, “On the direct product of closed operators,”Izv. Akad. Nauk SSSR, Ser. Mat., No. 1, 53–86 (1939).Google Scholar
  2. 2.
    Yu. M. Berezanskii and Yu. G. Kondrat'ev,Spectral Methods in Infinite-Dimensional Analysis [in Russian], Naukova Dumka, Kiev (1988);English translation: Kluwer AP, Dordrecht (1995).Google Scholar
  3. 3.
    M. Sh. Birman, A. M. Vershik, and M. Z. Solomyak, “Products of permutable spectral measures may be not countably additive,”Funkts. Anal. Prilozh.,13, No. 1, 61–62 (1979).Google Scholar
  4. 4.
    M. Reed and B. Simon,Methods of Modern Mathematical Physics, Academic Press, New York-San Francisco-London (1972–1979).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • V. O. Livinskii
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev

Personalised recommendations