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


Author: P. Gavruta
Journal: Proc. Amer. Math. Soc. 136 (2008), 3155-3158
MSC (2000): Primary 47A20; Secondary 47B99
DOI: https://doi.org/10.1090/S0002-9939-08-09463-X
Published electronically: 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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Additional Information

P. Gavruta
Affiliation: Department of Mathematics, University “Politehnica” of Timişoara, Piaţa Victoriei No. 2, 300006 Timişoara, Romania
Email: pgavruta@yahoo.com

DOI: https://doi.org/10.1090/S0002-9939-08-09463-X
Keywords: Operator, dilation, $\rho $-contraction
Received by editor(s): June 7, 2007
Published electronically: April 29, 2008
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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