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Cím:On the inclination of hyperinvariant subspaces of $C\sb{11}$- contractions.
Szerző:K\'erchy, L.
Forrás:Oper. Theory, Adv. Appl. 41, 345-351 (1989).
Nyelv:English
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 
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