On a class of non-Hermitian Hamiltonians with tridiagonal matrix representation

We show that some non-Hermitian Hamiltonian operators with tridiagonal matrix representation may be quasi Hermitian or similar to operators. In the class of discussed here transformation is given by a Hermitian, positive-definite, diagonal operator. there an important difference between open boundary conditions and periodic ones. illustrate theoretical results means two simple, widely used, models.