Advertisement

manuscripta mathematica

, Volume 29, Issue 2–4, pp 113–118 | Cite as

On the spectral kernel of symmetric extensions

  • Winfried Kaballo
  • Albert Schneider
Article
  • 18 Downloads

Abstract

In a Hilbert space H we consider closed and symmetric operators A and à with closed ranges such that A⊂Ã. We prove a necessary and sufficient condition for the existence of a closed and symmetric operator B with A⊂B⊂à the range of which is not closed. We show that this condition can be fulfilled and, by the way, we get a counter example to the assertion that the continuous part of the spectral kernel of a symmetric operator is contained in the corresponding part of a symmetric extension, as is claimed in the books of Achieser-Glasmann [1], Neumark [2] and Smirnow [3].

Keywords

Hilbert Space Number Theory Algebraic Geometry Topological Group Symmetric Operator 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Achieser, N.I., Glasmann, I.M.: Theorie der linearen Operatoren im Hilbertraum. Akademie-Verlag, Berlin 1968Google Scholar
  2. 2.
    Neumark, N.A.: Lineare Differentialoperatoren. Akademie-Verlag, Berlin 1967Google Scholar
  3. 3.
    Smirnow, W.I.: Lehrgang der höheren Mathematik V. Deutscher Verlag der Wissenschaften, Berlin 1967Google Scholar
  4. 4.
    Triebel, H.: Höhere Analysis. Deutscher Verlag der Wissenschaften, Berlin 1972Google Scholar
  5. 5.
    Weidmann, J.: Lineare Operatoren in Hilberträumen. Teubner, Stuttgart 1976Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Winfried Kaballo
    • 1
  • Albert Schneider
    • 1
  1. 1.Abteilung MathematikUniversität DortmundDortmund 50

Personalised recommendations