| Cím: | Contractions being weakly similar to unitaries. |
| Szerző: | K\'erchy, L\'aszl\'o |
| Forrás: | Advances in invariant subspaces and other results of operator theory, 9th Int. Conf. Oper. Theory, Timi\c{s}oara \& Herculane/Rom. 1984, Oper. Theory, Adv. Appl. 17, 187-200 (1986). |
| Nyelv: | English |
| Absztrakt: | [For the entire collection see Zbl 0579.00011.] \par
We call
a contraction T acting on a Hilbert space H to be weakly similar
to unitary if it can be found a system $\{H\sb n\}\sp{\infty}\sb{n=1}$
of hyperinvariant subspaces for T such that $T\vert H\sb n$ is
similar to unitary and $H\sb n\dot +(\bigvee\sb{k\ne n}H\sb k)=H$,
for every n, and $\cap\sb{n}(\bigvee\sb{k\ge n}H\sb k)=\{0\}$.
A criterion is given for a contraction to be weakly similar to
unitary, in terms of the characteristic function. The bicommutant
property Alg T$=\{T\}''$ is investigated in the case when T is
weakly similar to unitary and its characteristic function is
isometric on a set of positive measure. (Here Alg T denotes the
weakly closed algebra generated by T and the identity, and $\{$
$T\}$ '' stands for the bicommutant of T.) Finally, the cyclicity
of $C\sb{11}$-contractions is characterized. |
| Letöltés: | | Zentralblatt |