Weakly supercyclic operators

被引：35
|
作者：
Sanders, R [1 ]
机构：
[1] Bowling Green State Univ, Dept Math & Stat, Bowling Green, OH 43403 USA
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2004年 / 292卷 / 01期
关键词：
hypercyclic operator; supercyclic operator; hyponormal operator; bilateral weighted shift; unilateral weighted shift; weak topology;
D O I：
10.1016/j.jmaa.2003.11.049
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Inspired by a recent result that a weakly hypercyclic operator may fail to be norm hypercyclic, we show there exists a weakly supercyclic operator that fails to be norm supercyclic. Moreover, despite a classical result of Hilden and Wallen that every unilateral weighted backward shift is supercyclic, we show such an operator may have a weakly supercyclic vector that is not a norm supercyclic vector. In addition to these results, we extend a result of Kitai by showing a hyponormal operator cannot be weakly hypercyclic. (C) 2003 Elsevier Inc. All rights reserved.
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页码：148 / 159
页数：12
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