Opuscula Math. 37, no. 1 (2017), 65-80
http://dx.doi.org/10.7494/OpMath.2017.37.1.65

Opuscula Mathematica

# Towards theory of C-symmetries

S. Kuzhel
V. Sudilovskaya

Abstract. The concept of $$\mathcal{C}$$-symmetry originally appeared in $$\mathcal{PT}$$-symmetric quantum mechanics is studied within the Krein spaces framework.

Keywords: Krein space, $$J$$-self-adjoint operator, $$J$$-symmetric operator, Friedrichs extension, $$\mathcal{C}$$-symmetry.

Mathematics Subject Classification: 47A55, 47B25, 47A57, 81Q15.

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• S. Kuzhel
• AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, Poland
• V. Sudilovskaya
• Kyiv Vocational College, Kyiv, Ukraina
• Communicated by Aurelian Gheondea.
• Revised: 2016-09-15.
• Accepted: 2016-10-07.
• Published online: 2016-12-14.