| Absztrakt: | Let T be a $C\sb{11}$-contraction on a Hilbert space H, i.e.
$\lim\sb{n\to \infty}\Vert T\sp nx\Vert \ne 0\ne \lim\sb{n\to
\infty}\Vert T\sp{*n}x\Vert$ for every nonzero $x\in H$. Then
T is quasisimilar to a unitary operator U. Let $Hyplat\sb 1T$
denote the set of all hyperinvariant subspaces M of T such that
$T\vert M$ is of class $C\sb{11}$. It is known that there is
a unique lattice isomorphism q from $Hyplat\sb 1T$ to Hyplat
U $(=$ the hyperinvariant subspace lattice of U) with the proerty
that $T\vert M$ is quasisimilar to $U\vert q(M)$ for every $M\in
Hyplat\sb 1T.$ \par
In this paper the author investigates the
angle between $q\sp{-1}(N\sb 1)$ and $q\sp{-1}(N\sb 2)$ for disjoint
spectral subspaces $N\sb 1$ and $N\sb 2$ of U. then he answers
in the negative the following question posed by {\it L. A. Fialkow}
[J. Oper. Theory 14, 215-238 (1985; Zbl 0613.47015)]: if A and
B are quasisimilar operators and the spectrum $\sigma$ (A) of
A is the disjoint union of two closed sets $\sigma\sb 1$ and
$\sigma\sb 2$, does B have complementary invariant subspaces
$M\sb 1$ and $M\sb 2$ such that $B\vert M\sb i$ is quasisimilar
to the restriction of A to the Riesz spectral subspace corresponding
to $\sigma\sb i$ $(i=1,2)?$}
\RV{K.Takahashi |