Reality and non-reality of the spectrum

of PT-symmetric operators: Operator-theoretic

criteria

 

E CALICETI* and S GRAFFI

Dipartimento di Matematica, Universit\`a di Bologna, and INFN, Bologna, Italy

*Corresponding author. E-mail: caliceti@dm.unibo.it

 

Abstract. We generalize some recently established criteria for the

reality and non-reality of the spectrum of some classes of

PT-symmetric Schr\"odinger operators. The criteria include cases of

discrete spectra and continuous ones.

 

Keywords. Perturbation theory; $\PT$ symmetry; periodic potentials.

 

PACS Nos 03.65.-w; 03.65.Ca; 03.65.Ge; 02.30.Tb; 03.65.Nk