Pseudohermitian Hamiltonians, time-reversal invariance and Kramers   degeneracy
  A necessary and sufficient condition in order that a (diagonalizable) pseudohermitian operator admits an antilinear symmetry T such that T^{2}=-1 is proven. This result can be used as a quick test on the T-invariance properties of pseudohermitian Hamiltonians, and such test is indeed applied, as an example, to the Mashhoon-Papini Hamiltonian. 
G. Scolarici and L. Solombrino