Hilbert space models and Blaschke frames

For a finite Blaschke product $B$ and for an isometry $V$ on an infinite-dimensional separable complex Hilbert space $\mathcal{H}$ we study a sequence $(b_m)_{m=1}^\infty$ of vectors in $\mathcal{H}$, defined by $b_m = B(V^*)e_m$, where $(e_m)_{m=1}^\infty$ is an orthonormal basis in $\mathcal{H}$.