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On generalized selfadjoint operators on scales of Hilbert spaces

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Abstract

We consider examples of generalized selfadjoint operators that act from a positive Hilbert space to a negative space. Such operators were introduced and studied in [1]. We give examples of selfadjoint operators on the principal Hilbert space $H_ 0$ that, being considered as operators from the positive space $H_ + \subset H_ 0$ into the negative space $H_ - \supset H_ 0$, are not essentially selfadjoint in the generalized sense.

Key words: Selfadjoint operators, generalized selfadjoint operators, Hilbert space rigging.


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Article Information

TitleOn generalized selfadjoint operators on scales of Hilbert spaces
SourceMethods Funct. Anal. Topology, Vol. 17 (2011), no. 3, 193-198
MathSciNet MR2857721
CopyrightThe Author(s) 2011 (CC BY-SA)

Authors Information

Yu. M. Berezansky
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

J. Brasche
Institute of Mathematics, TU Clausthal, 1 Erzstr., Clausthal-Zellerfeld, 38678, Germany

L. P. Nizhnik
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine 


Citation Example

Yu. M. Berezansky, J. Brasche, and L. P. Nizhnik, On generalized selfadjoint operators on scales of Hilbert spaces, Methods Funct. Anal. Topology 17 (2011), no. 3, 193-198.


BibTex

@article {MFAT587,
    AUTHOR = {Berezansky, Yu. M. and Brasche, J. and Nizhnik, L. P.},
     TITLE = {On generalized selfadjoint operators on scales of Hilbert spaces},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {17},
      YEAR = {2011},
    NUMBER = {3},
     PAGES = {193-198},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=587},
}


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