Universal and chaotic multipliers on spaces of operators

被引：52

作者：

Bonet, J ^{[1
]}

Martínez-Giménez, F

Peris, A

机构：

[1] Univ Politecn Valencia, ETS Arquitectura, Dept Matemat Aplicada, E-46071 Valencia, Spain

[2] Univ Politecn Valencia, ETS Arquitectura, Dept Matemat Aplicada, E-46071 Valencia, Spain

[3] Univ Politecn Valencia, ETSI Agron, Dept Matemat Aplicada, E-46071 Valencia, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2004年 / 297卷 / 02期

关键词：

hypercyclic vectors; multipliers on Banach algebras; chaotic dynamics; universality; Frechet spaces; (DF)-spaces;

D O I：

10.1016/j.jmaa.2004.03.073

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We use tensor product techniques to study universality, hypercyclicity and chaos of multipliers defined on operator ideals and of multiplication operators on the space of all continuous and linear operators, thus continuing the work of Kit Chan. We also obtain the first examples of outer multipliers on a Banach algebra which are chaotic in the sense of Devaney, and prove sufficient conditions for the existence of closed subspaces of universal vectors for operators between Frechet spaces. (C) 2004 Elsevier Inc. All rights reserved.

引用

页码：599 / 611

页数：13

共 33 条

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

Ansari, SI .

JOURNAL OF FUNCTIONAL ANALYSIS, 1997, 148 (02) :384-390

[2] ON DEVANEY DEFINITION OF CHAOS [J].

BANKS, J ;

BROOKS, J ;

CAIRNS, G ;

DAVIS, G ;

STACEY, P .

AMERICAN MATHEMATICAL MONTHLY, 1992, 99 (04) :332-334

[3]

BEMALGONZALEZ L, 1999, P AM MATH SOC, V127, P1003

[4] The range of operators on von Neumann algebras [J].

Bermúdez, T ;

Kalton, NJ .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 130 (05) :1447-1455

[5] The Hypercyclicity Criterion for sequences of operators [J].

Bernal-González, L ;

Grosse-Erdmann, KG .

STUDIA MATHEMATICA, 2003, 157 (01) :17-32

[6] Hereditarily hypercyclic operators [J].

Bès, J ;

Peris, A .

JOURNAL OF FUNCTIONAL ANALYSIS, 1999, 167 (01) :94-112

[7]

Birkhoff GD, 1929, CR HEBD ACAD SCI, V189, P473

[8] SPACES OF OPERATORS BETWEEN FRECHET SPACES [J].

BONET, J ;

LINDSTROM, M .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1994, 115 :133-144

[9] A Banach space which admits no chaotic operator [J].

Bonet, J ;

Martínez-Giménez, F ;

Peris, A .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2001, 33 :196-198

[10] Hypercyclic operators on non-normable Frechet spaces [J].

Bonet, J ;

Peris, A .

JOURNAL OF FUNCTIONAL ANALYSIS, 1998, 159 (02) :587-595

← 1 2 3 4 →