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# On generalized selfadjoint operators on scales of Hilbert spaces

### 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.

### 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},
URL = {http://mfat.imath.kiev.ua/article/?id=587},
}