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Cím:On the spectra of contractions belonging to special classes.
Szerző:K\'erchy, L\'asl\'o
Forrás:J. Funct. Anal. 67, 153-166 (1986).
Nyelv:English
Absztrakt:Let T be a contraction acting on the Hilbert space H. Let us assume that T is of class $C\sb{10}$ that is $\lim\sb{n\to \infty}\Vert T\sp nh\Vert \ne 0=\lim\sb{n\to \infty}\Vert T\sp{*n}h\Vert$, for every nonzero vector h. Then a new scalar product can be introduced in H by $<h,k>\sb{\sim}=\lim\sb{n\to \infty}<T\sp nh,T\sp nk>$. T acts as an isometry on the inner product space $(H,<\cdot,\cdot >\sb{\sim})$. Let $\tilde T$ denote the minimal unitary extension of this isometry acting on the Hilbert space $\tilde H.$ The main result of the paper is a complete characterization of the possible spectra of a $C\sb{10}$- contraction T and its minimal unitary extension $\tilde T.$ The theorem is analogous to the one obtained for $C\sb{11}$-contractions in the work [Proc. Amer. Math. Soc. 95, 412-418 (1985)], jointly with {\it H. Bercovici}; however the proof is more difficult. 
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