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On commuting symmetric operators


In this paper we present some conditions for a pair of commuting symmetric operators with a joint invariant dense domain in a Hilbert space, to have a commuting self-adjoint extension in the same space. The remarkable Godic-Lucenko theorem allows to get a convenient description of all such extensions.

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TitleOn commuting symmetric operators
SourceMethods Funct. Anal. Topology, Vol. 18 (2012), no. 2, 198-200
MathSciNet   MR2978195
zbMATH 1258.47037
CopyrightThe Author(s) 2012 (CC BY-SA)

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S. M. Zagorodnyuk
School of Mathematics and Mechanics, Karazin Kharkiv National University, 4 Svobody sq., Kharkiv, 61077, Ukraine

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S. M. Zagorodnyuk, On commuting symmetric operators, Methods Funct. Anal. Topology 18 (2012), no. 2, 198-200.


@article {MFAT645,
    AUTHOR = {Zagorodnyuk, S. M.},
     TITLE = {On commuting symmetric operators},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {18},
      YEAR = {2012},
    NUMBER = {2},
     PAGES = {198-200},
      ISSN = {1029-3531},
  MRNUMBER = {MR2978195},
 ZBLNUMBER = {1258.47037},
       URL = {},

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