Elements with generalized bounded conjugation orbits

被引：9
作者：
Drissi, D
Mbekhta, M
机构：
[1] Kuwait Univ, Fac Sci, Dept Math & Comp Sci, Safat 13060, Kuwait
[2] Univ Lille 1, CNRS, UMR 8524, F-59655 Villeneuve Dascq, France
[3] Univ Lille 1, UFR Math, F-59655 Villeneuve Dascq, France
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2001年 / 129卷 / 07期
关键词：
bounded conjugation orbit; spectrum; spectral radius;
D O I：
10.1090/S0002-9939-01-05945-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For a pair of linear bounded operators T and A on a complex Banach space X, if T commutes with A, then the orbits { A(n)TA(-n)} of T under A 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.
引用
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页码：2011 / 2016
页数：6
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