Classical orthogonal polynomials and matrix polynomials being orthogonal with respect to some Hermitean positive definite matrix of measures share several properties, e.g., three term recurrencies, Christoffel--Darboux formulas; there are connections to the triangular decomposition of the (inverse) moment matrix and to eigenvalue--problems for the banded matrix of recurrence coefficients. Also, a connection between these orthogonal polynomials and the spectral analysis of selfadjoint operators is well--known.

In this paper we study these aspects for rectangular matrix valued measures. In particular, we establish a caracterization in terms of matrix Padé approximants of the spectrum and the resolvent set of a difference operator, i.e., a not necessarily selfadjoint, but bounded operator which may be represented as a biinfinite banded matrix. As an application, we give convergence theorems of matrix Padé approximants.