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Cím:On the functional calculus of contractions with nonvanishing unitary asymptotes.
Szerző:K\'erchy, L.
Forrás:Mich. Math. J. 37, No.3, 323-338 (1990).
Nyelv:English
Absztrakt:Let $T$ be a contraction on a Hilbert space $H$. There exist a Hilbert space $H'$, a unitary operator $T'$ on $H'$, and an operator $X: H\to H'$ and such that $T'X=XT$ and such that the triplet $(H',T',X)$ is `universal' with these properties. The author calls $T'$ the unitary asymptote of $T$. If $T$ is an absolute continuous contraction then $T'$ has absolutely continuous spectral measure, and hence there is a Borel set $\Gamma$ such that arclength on $\Gamma$ is a saclar measure for $T'$.\par The main purpose of this article is to produce a new factorization technique in the theory of dual algebras. The author illustrates this technique by providing, along with some new results, a new proof of the following result of {\it B. Chevreau}, {\it G. Exner} and {\it C. Pearcy} [Mich. Math. J. 36, 29-62 (1989; Zbl 0677.47001)]: given $\varepsilon>0$ and $f\in L\sp 1(\Gamma)$, there exist vectors $x,y\in H$ such that $\Vert x\Vert\Vert y\Vert\leq(1+\varepsilon)\Vert f\Vert\sb 1$ and $(p(T)x,y)=\int\sb \Gamma pf$ for every polynomial $p$ in one variable.} \RV{H.Bercovici (Bloomington) 
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