Similarity transformations and non-hermitian hamiltonians with real spectra

Similarity transformations link hermitian with non-hermitian operators while preserving the spectrum, thus providing a means for the generation of exactly-solvable non-hermitian hamiltonians with real spectra. Pairs of isospectral partners can be set in a matrix arrangement similar to the superhamiltonian of SUSY-QM, describing a system with an underlying sl(2, C ) graded algebra. A case is discussed where orthogonality, normalizability and the definition of the inner product are preserved by the similarity transformation. The resulting hamiltonians are time-reversal invariant and weakly-pseudo-hermitian but not necessarily PT-symmetric.