| 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) |
| Letöltés: | | Zentralblatt |