Intertwining operators between different Hilbert spaces: connection with frames

In this paper we generalize a strategy recently proposed by the author concerning intertwining operators. In particular, we discuss the possibility of extending our previous results in such a way to construct ͑almost͒ isospectral self-adjoint opera- tors living in different Hilbert spaces. Many examples are discussed in details. Many of them arise from the theory of frames in Hilbert spaces, others from the so-called g-frames.