Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

On a problem of Bernard Chevreau concerning the $\rho$ -contractions

Author(s): P. Gavruta
Journal: Proc. Amer. Math. Soc. 136 (2008), 3155-3158.
MSC (2000): Primary 47A20; Secondary 47B99
Posted: April 29, 2008
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Abstract: We prove new results for the operators of class $C_{\rho} (\rho >0)$ on Hilbert spaces defined by B. Sz.-Nagy and C. Foiaş. The main result is an answer to a problem posed in 2006 by B. Chevreau: Let $p\geq 2$ be a natural number and $T \in \mathrm{L}(\mathcal{H})$ ; if there exists $\rho_{0} >0$ such that $T^{p} \in C_{\rho_0}$ , then necessarily is $T \in \bigcup_{\rho>0}C_{\rho}$ ?

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