## A Krein space approach to $$PT$$ symmetry.(English)Zbl 1162.81375

Czech. J. Phys. 54, No. 10, 1113-1120 (2004); corrigendum ibid. No. 9, 1063-1064 (2006).
Summary: In this note we apply Krein space methods to $$PT$$-symmetric problems to obtain conditions for the spectrum to be real and estimates of the number of non-real spectral points.

### MSC:

 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 47A55 Perturbation theory of linear operators 47B50 Linear operators on spaces with an indefinite metric 47N50 Applications of operator theory in the physical sciences

### Keywords:

PT-symmetry; spectrum; Krein space
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