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Contractions with countable spectra and unicity properties of closed countable sets of the circle. (Contractions à spectre dénombrable et propriétés d’unicité des fermés dénombrables du cercle.) (French) Zbl 0766.47002
On montre que si \(T\) est une contraction à spectre dénombrable et telle que, pour tout \(\varepsilon>0\) \(\| T^{- 1}\|=O(e^{\varepsilon n^{1/2}})\) \((n\to+\infty)\), alors \(T\) est une isometrie. On montre aussi que ce résultat est lié à une propriété d’unicité forte des fermés dénombrable du cercle unité.
Reviewer: M.Zarrabi

MSC:
47A30 Norms (inequalities, more than one norm, etc.) of linear operators
42A63 Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization
43A45 Spectral synthesis on groups, semigroups, etc.
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