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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A Katznelson-Tzafriri type theorem in Hilbert spaces


Author: Zoltán Léka
Journal: Proc. Amer. Math. Soc. 137 (2009), 3763-3768
MSC (2000): Primary 47A35, 46B08; Secondary 46M07, 47B99
Published electronically: May 27, 2009
MathSciNet review: 2529885
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Abstract: Our aim is to characterize, via an ergodic condition, the norm convergence $ \lim_{n \rightarrow \infty} \Vert T^nQ\Vert = 0$ when $ T$ is a power-bounded operator on a Hilbert space and $ Q$ commutes with $ T.$ We shall also prove that if $ f \in A^+(\mathbb{T})$ and $ Q = f(T),$ the given condition is equivalent to the vanishing of $ f$ on the peripheral spectrum of $ T.$


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Additional Information

Zoltán Léka
Affiliation: Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary
Email: lzoli@math.u-szeged.hu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09939-0
PII: S 0002-9939(09)09939-0
Keywords: Ultrapower, stablity of operators, uniform ergodicity
Received by editor(s): September 2, 2008
Received by editor(s) in revised form: February 20, 2009
Published electronically: May 27, 2009
Additional Notes: This study was partially supported by Hungarian NSRF (OTKA) grant No. T 49846 and by the Marie Curie “Transfer of Knowledge” programme, project TODEQ
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.