On weak decay rates and uniform stability of bounded linear operators

被引：5
作者：
Glueck, Jochen [1 ]
机构：
[1] Univ Ulm, Inst Appl Anal, D-89069 Ulm, Germany
来源：
ARCHIV DER MATHEMATIK | 2015年 / 104卷 / 04期
关键词：
Weak stability; Uniform stability; Spectral radius; Decay rates; Domination; Principal ideal; EXPONENTIAL STABILITY; ORBITS;
D O I：
10.1007/s00013-015-0746-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider a bounded linear operator T on a complex Banach space X and show that its spectral radius r(T) satisfies r(T) < 1 if all sequences () are, up to a certain rearrangement, contained in a principal ideal of the space c (0) of sequences which converge to 0. From this result we obtain generalizations of theorems of Weiss and van Neerven. We also prove a related result on C (0)-semigroups.
引用
收藏
页码：347 / 356
页数：10
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