Disjointness in hypercyclicity

被引：102

作者：

Bes, Juan ^{[1
]}

Peris, Alfredo

机构：

[1] Bowling Green State Univ, Dept Math & Stat, Bowling Green, OH 43403 USA

[2] Univ Politecn Valencia, Dept Matemat Aplicada, ETS Arquitectura, E-46022 Valencia, Spain

[3] Univ Politecn Valencia, IMPA, ETS Arquitectura, E-46022 Valencia, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2007年 / 336卷 / 01期

关键词：

hypercyclic vectors; hypercyclic operators;

D O I：

10.1016/j.jmaa.2007.02.043

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a notion of disjointness for finitely many hypercyclic operators acting on a common space, notion that is weaker than Furstenberg's disjointness of fluid flows. We provide a criterion to construct disjoint hypercyclic operators, that generalizes some well-known connections between the Hypercyclicity Criterion, hereditary hypercyclicity and topological mixing to the setting of disjointness in hypercyclicity. We provide examples of disjoint hypercyclic operators for powers of weighted shifts on a Hilbert space and for differentiation operators on the space of entire functions on the complex plane. (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：297 / 315

页数：19

共 25 条

[11] 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

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

GODEFROY, G ;

SHAPIRO, JH .

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

[13]

Grivaux S, 2005, J OPERAT THEOR, V54, P147

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

Grosse-Erdmann, KG .

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

[15]

GROSSEERDMAN KG, 1987, MITT MATH SEM GIESSE, V176

[16]

GROSSEERDMANN KG, 2003, RACSAM REV R ACAD A, V97, P273

[17]

Herrero D. A., 1992, J OPERATOR THEORY, V28, P93

[18]

HILLE E, 1962, ANAL FUNTION THEORY, V2

[19]

Kitai C., 1982, THESIS U TORONTO

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

León-Saavedra, F ;

Müller, V .

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

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