Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
Published electronically: April 29, 2008
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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}$?

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47A20, 47B99

Retrieve articles in all journals with MSC (2000): 47A20, 47B99

Additional Information

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

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.