Non-Hermitian Hamiltonians and similarity transformations

We show that similarity (or equivalent) transformations enable one to construct non-Hermitian operators with real spectrum. In this way we can also prove and generalize the results obtained by other authors by means of a gauge-like transformation and its generalization. Such similarity transformations also reveal the connection with pseudo-Hermiticity in a simple and straightforward way. In addition to it we consider the positive and negative eigenvalues of a three-parameter non-Hermitian oscillator.