-symmetry and weak pseudo-hermiticity

Abstract

For an invertible (bounded) linear operator acting in a Hilbert space , we consider the consequences of the -symmetry of a non-hermitian Hamiltonian where is the time-reversal operator. If H is symmetric in the sense that , then -symmetry is equivalent to -weak-pseudo-hermiticity. But in general this equivalence does not hold. We show this using some specific examples. Among these is a large class of non--symmetric Hamiltonians that share the spectral properties of -symmetric Hamiltonians.