On a problem of Bernard Chevreau concerning the 𝜌-contractions

Găvruţa, P.

doi:10.1090/S0002-9939-08-09463-X

On a problem of Bernard Chevreau concerning the $\rho$-contractions
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Proc. Amer. Math. Soc. 136 (2008), 3155-3158 Request permission

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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