Kérchy László honlapja

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Cím:Polynomially bounded operators whose spectrum on the unit circle has measure zero.
Szerző:K\'erchy, L.; van Neerven, J.
Forrás:Acta Sci. Math. 63, No.3-4, 551-562 (1997).
Nyelv:English
Absztrakt:The authors generalize a result of the Sz.-Nagy-Foias theory of operators by verifying the following result (Theorem 1.2): \par If $T$ is a polynomially bounded operator on a complex Banach space which belongs to the class $C_{1 \bullet}$ and $\sigma(T)\cap \partial \bold D$ has Lebesgue measure zero, then $T$ is similar to an invertible isometry. \par The proof is based on the use of Banach limits and continuous functional calculus. Theorem 1.4 treats a local version of this result. The presented methods are used to extend the Esterle-Strouse-Zouakia version of the well-known Katznelson-Tzafriri theorem. One-parameter semigroups of Hilbert space contractions are also considered.} \RV{Lajos Moln\'ar (Debrecen) 
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