Absztrakt: | Let $T\in {\cal L} ({\cal H})$ be the absolutely continuous contraction
such that the spectral multiplicity function of its unitary asymptote
$T^{(a)}$ is at least $n$ $(1\leq n\leq \aleph_0)$ almost everywhere
on a subset $\gamma$ (with positive measure) of the unit circle
${\bold T}$. Let ${\cal G}_n$ be an $n$-dimensional Hilbert space
and let $J_{n, \gamma}$ denote the canonical embedding of the
Hilbert space $H^2 ({\cal G}_n)$ into $\chi_\gamma L^2 ({\cal
G}_n)$. It is shown that, given any positive $\varepsilon$, there
exists a factorization $J_{n, \gamma}= ZY$ such that the mappings
$Y\in {\cal L} (H^2 ({\cal G}_n), {\cal H})$ and $Z\in {\cal
L} ({\cal H}, \chi_\gamma L^2 ({\cal G}_n))$ intertwine $T$ with
the operators of multiplication by the identical function on
the corresponding spaces, and the product: $|Y||Z|\leq \sqrt{2}+
\varepsilon$. As a consequence, we obtain that the unilateral
shift $S_n$ of multiplicity $n$ can be completely injected into
$T$ and that $T$ has the property $({\bold A}_{n, \aleph_0} (\gamma))$
introduced in the theory of dual algebras. It follows furthermore
that in the special case $\gamma= {\bold T}$ the contraction
$T$ has an invariant subspace ${\cal H}'$ such that the restriction
$T\mid {\cal H}'$ is similar to $S_n$. |