Kérchy László honlapja

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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).
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. 
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