On linear chaos in function spaces

被引：1

作者：

Jimenez, John M. ^{[2
]}

Markin, Marat, V ^{[1
]}

机构：

[1] Calif State Univ Fresno, Dept Math, 5245 N Backer Ave,M-S PB 108, Fresno, CA 93740 USA

[2] De Anza Coll, Dept Math, 21250 Stevens Creek Blvd, Cupertino, CA 95014 USA

来源：

DEMONSTRATIO MATHEMATICA | 2022年 / 55卷 / 01期

关键词：

hypercyclic vector; periodic point; hypercyclic operator; chaotic operator; spectrum; OPERATORS;

D O I：

10.1515/dema-2022-0008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that, in L-p(0, infinity) (1 <= p < infinity) , bounded weighted translations as well as their unbounded counterparts are chaotic linear operators. We also extend the unbounded case to C-0[0, infinity) and describe the spectra of the weighted translations provided the underlying spaces are complex.

引用

页码：119 / 135

页数：17

共 15 条

[1]

[Anonymous], 2011, Linear chaos

[2] Chaos on function spaces [J].

Aron, RM ;

Seoane-Sepúlveda, JB ;

Weber, A .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2005, 71 (03) :411-415

[3]

Bayart F, 2009, CAMB TRACT MATH, P1, DOI 10.1017/CBO9780511581113

[4] Chaotic unbounded differentiation operators [J].

Bès, J ;

Chan, KC ;

Seubert, SM .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2001, 40 (03) :257-267

[5] Chaos for semigroups of unbounded operators [J].

deLaubenfels, R ;

Emamirad, H ;

Grosse-Erdmann, KG .

MATHEMATISCHE NACHRICHTEN, 2003, 261 :47-59

[6]

Devaney Robert, 2018, An introduction to chaotic dynamical systems

[7]

Dunford N., 1958, Linear operators. I. General theory

[8] UNIVERSAL VECTORS FOR OPERATORS ON SPACES OF HOLOMORPHIC-FUNCTIONS [J].

GETHNER, RM ;

SHAPIRO, JH .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 100 (02) :281-288

[9] OPERATORS WITH DENSE, INVARIANT, CYCLIC VECTOR MANIFOLDS [J].

GODEFROY, G ;

SHAPIRO, JH .

JOURNAL OF FUNCTIONAL ANALYSIS, 1991, 98 (02) :229-269

[10]

Kitai C., 1982, Thesis

← 1 2 →