SUPERCYCLIC AND CESARO HYPERCYCLIC WEIGHTED TRANSLATIONS ON GROUPS

被引：11

作者：

Chen, Chung-Chuan ^{[1
]}

机构：

[1] Natl Taichung Univ Educ, Dept Math Educ, Taichung 403, Taiwan

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2012年 / 16卷 / 05期

关键词：

Supercyclic operators; Cesaro hypercyclic operators; Locally compact groups; L-p-spaces; OPERATORS; SHIFTS;

D O I：

10.11650/twjm/1500406799

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a locally compact group and let 1 <= p < infinity. We characterize supercyclic weighted translation operators on the Lebesgue space L-p(G) in terms of the weight. Using this result, the characterization for Cesaro hypercyclic weighted translation operators is given. We also determine when scalar multiples of weighted translation operators are hypercyclic and topologically mixing, and show, for any weighted translation operator T, beta T is mixing for all beta is an element of (1, 4) if T and 4T are mixing.

引用

页码：1815 / 1827

页数：13

共 14 条

[1]

[Anonymous], 1979, ABSTRACT HARMONIC AN

[2] MULTIPLES OF HYPERCYCLIC OPERATORS [J].

Badea, Catalin ;

Grivaux, Sophie ;

Muller, Vladimir .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 137 (04) :1397-1403

[3] HYPERCYCLIC WEIGHTED TRANSLATIONS ON GROUPS [J].

Chen, C. ;

Chu, C-H. .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 139 (08) :2839-2846

[4] HYPERCYCLICITY OF WEIGHTED CONVOLUTION OPERATORS ON HOMOGENEOUS SPACES [J].

Chen, C. ;

Chu, C-H .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 137 (08) :2709-2718

[5] Chaotic weighted translations on groups [J].

Chen, Chung-Chuan .

ARCHIV DER MATHEMATIK, 2011, 97 (01) :61-68

[6]

Grosse-Erdmann K., 2003, RACSAM REV R ACAD CI, V97, P273

[7] Universal families and hypercyclic operators [J].

Grosse-Erdmann, KG .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 36 (03) :345-381

[8] ON CENTRAL TOPOLOGICAL GROUPS [J].

GROSSER, S ;

MOSKOWIT.M .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1967, 127 (02) :317-&

[9] Hypercyclic, mixing, and chaotic C0-semigroups induced by semiflows [J].

Kalmes, T. .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2007, 27 :1599-1631

[10] Rotations of hypercyclic and supercyclic operators [J].

León-Saavedra, F ;

Müller, V .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2004, 50 (03) :385-391

← 1 2 →