HYPERCYCLICITY OF WEIGHTED CONVOLUTION OPERATORS ON HOMOGENEOUS SPACES

被引：24

作者：

Chen, C. ^{[1
]}

Chu, C-H ^{[1
]}

机构：

[1] Univ London, Sch Math Sci, London E1 4NS, England

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 137卷 / 08期

关键词：

Hypercyclic operator; topologically mixing operator; convolution; homogeneous space; L-p-space; BANACH-SPACES; CHAOTIC SEMIGROUPS; CRITERION; INVARIANT; SEQUENCES;

D O I：

10.1090/S0002-9939-09-09889-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let 1 <= p <= infinity. We show that a weighted translation operator oil the LP space of a homogeneous space is hypercyclic under some condition on the weight. This condition is also necessary in the discrete case and is equivalent to hereditary hypercyclicity of the operator. The condition call be strengthened to characterise topologically mixing weighted translation operators on discrete spaces.

引用

页码：2709 / 2718

页数：10

共 28 条

[1]

[Anonymous], 1952, Journal d'Analyse Mathematique, DOI DOI 10.1007/BF02786968

[2] Existence of hypercyclic operators on topological vector spaces [J].