  For a fixed $p \in \mathbb{N}$, sequences of polynomials $\{P_n\}$, $n \in
\mathbb{N}$, defined by a $(p+2)$-term recurrence relation are related to
several topics in Approximation Theory. A $(p+2)$-banded matrix $J$ determines
the coefficients of the recurrence relation of any of such sequences of
polynomials. The connection between these polynomials and the concept of
orthogonality has been already established through a $p$-dimension vector of
functionals. This work goes further in this topic by analyzing the relation
between such vectors for the set of sequences $\{P_n^{(j)}\}$, $n \in N$,
associated with the Darboux transformations $J^{(j)}$, $j=1, ..., p,$ of a
given $(p+2)$-banded matrix $J$.

Functional Analysis