Elements with generalized bounded conjugation orbits

Authors:
Driss Drissi and Mostafa Mbekhta

Journal:
Proc. Amer. Math. Soc. **129** (2001), 2011-2016

MSC (2000):
Primary 47B10, 47B15

Published electronically:
January 17, 2001

MathSciNet review:
1825911

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Abstract | References | Similar Articles | Additional Information

Abstract: For a pair of linear bounded operators and on a complex Banach space , if commutes with then the orbits of under are uniformly bounded. The study of the converse implication was started in the 1970s by J. A. Deddens. In this paper, we present a new approach to this type of question using two localization theorems; one is an operator version of a theorem of tauberian type given by Katznelson-Tzafriri and the second one is on power-bounded operators by Gelfand-Hille. This improves former results of Deddens-Stampfli-Williams.

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Additional Information

**Driss Drissi**

Affiliation:
Department of Mathematics and Computer Science, Faculty of Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

Email:
drissi@mcs.sci.kuniv.edu.kw

**Mostafa Mbekhta**

Affiliation:
UMR-CNRS 8524 & UFR de Mathematiques, Université de Lille I, F-59655, Villeneuve d’asq, France

Email:
Mostafa.Mbekhta@univ-lille1.fr

DOI:
https://doi.org/10.1090/S0002-9939-01-05945-7

Keywords:
Bounded conjugation orbit,
spectrum,
spectral radius

Received by editor(s):
November 1, 1999

Published electronically:
January 17, 2001

Additional Notes:
Research of the first author partially supported by grants from Kuwait University.

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2001
American Mathematical Society