Reality and non-reality of
the spectrum
of PT-symmetric operators:
Operator-theoretic
criteria
E CALICETI* and
Dipartimento di
Matematica, Universit\`a di Bologna, and INFN,
*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