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Elements with generalized bounded conjugation orbits
Author(s):
Driss
Drissi;
Mostafa
Mbekhta
Journal:
Proc. Amer. Math. Soc.
129
(2001),
2011-2016.
MSC (2000):
Primary 47B10, 47B15
Posted:
January 17, 2001
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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.
References:
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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:
10.1090/S0002-9939-01-05945-7
PII:
S 0002-9939(01)05945-7
Keywords:
Bounded conjugation orbit,
spectrum,
spectral radius
Received by editor(s):
November 1, 1999
Posted:
January 17, 2001
Additional Notes:
Research of the first author partially supported by grants from Kuwait University.
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2001,
American Mathematical Society
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