  A particular case of [07] was generalized from contractions to polynomially
bounded operators in [G19]. Namely, it is proved in [G19] that if the unitary
asymptote of a polynomially bounded operator $T$ contains the bilateral shift
of multiplicity $1$, then there exists an invariant subspace $\mathcal M$ of
$T$ such that $T|_{\mathcal M}$ is similar to the unilateral shift of
multiplicity $1$. In the present paper, some corollaries of this result are
given. In particular, reflexivity of polynomially bounded operators described
above is proved.
