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.
Full Text
Article Information
| Title | On generalized selfadjoint operators on scales of Hilbert spaces |
| Source | Methods Funct. Anal. Topology, Vol. 17 (2011), no. 3, 193-198 |
| MathSciNet |
MR2857721 |
| Copyright | The 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},
MRNUMBER = {MR2857721},
URL = {http://mfat.imath.kiev.ua/article/?id=587},
}
