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

Langer, Heinz; Tretter, Christiane

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