On generalized selfadjoint operators on scales of Hilbert spaces

Authors

  • L. P. Nizhnik Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine
  • J. F. Brasche Institute of Mathematics, TU Clausthal, 1 Erzstr., Clausthal-Zellerfeld, 38678, Germany
  • Yu. M. Berezansky Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine  https://orcid.org/0000-0002-3298-0133

DOI:

Keywords:

Selfadjoint operators, generalized selfadjoint operators, Hilbert space rigging

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.

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Published

2011-09-25

Issue

Vol. 17 No. 3 (2011)

Section

Articles

How to Cite

Nizhnik, L. P., et al. “On Generalized Selfadjoint Operators on Scales of Hilbert Spaces”. Methods of Functional Analysis and Topology, vol. 17, no. 3, Sept. 2011, pp. 193-8, https://zen.imath.kiev.ua/index.php/mfat/article/view/483.