On generalized selfadjoint operators on scales of Hilbert spaces - Nizhnik, L. P.; Brasche, J. F.; Berezansky, Yu. M. (Methods of Functional Analysis and Topology, 2011)
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_ + H_ 0 into the negative space H_ - H_ 0, are not essentially selfadjoint in the generalized sense.