Common hypercyclic vectors for multiples of backward shift

被引：55

作者：

Abakumov, E

Gordon, J

机构：

[1] Univ Marne La Vallee, Equipe Anal & Math Appl, F-77454 Marne La Vallee 2, France

[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2003年 / 200卷 / 02期

关键词：

hypercyclic vector; backward shift;

D O I：

10.1016/S0022-1236(02)00030-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that l(2) contains vectors which are hypercyclic simultaneously for all multiples of the backward shift operator by constants of absolute value greater than 1. The set of such vectors is dense G(delta). (C) 2002 Elsevier Science (USA). All rights reserved.

引用

页码：494 / 504

页数：11

共 11 条

[1] Birkhoff GD, 1929, CR HEBD ACAD SCI, V189, P473
[2] INVARIANT-MANIFOLDS OF HYPERCYCLIC VECTORS
BOURDON, PS
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 118 (03) : 845 - 847
[3] BOURDON PS, 1990, MICH MATH J, V37, P71
[4] COMMON CYCLIC ENTIRE-FUNCTIONS FOR PARTIAL-DIFFERENTIAL OPERATORS
CHAN, KC
[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 1990, 13 (01) : 132 - 137
[5] COMMON CYCLIC VECTORS FOR OPERATOR-ALGEBRAS ON SPACES OF ANALYTIC-FUNCTIONS
CHAN, KC
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1988, 37 (04) : 919 - 928
[6] OPERATORS WITH DENSE, INVARIANT, CYCLIC VECTOR MANIFOLDS
GODEFROY, G
SHAPIRO, JH
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1991, 98 (02) : 229 - 269
[7] Universal families and hypercyclic operators
Grosse-Erdmann, KG
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 36 (03) : 345 - 381
[8] MacLane G.R., 1952, J ANAL MATH, V2, P72
[9] ON ORBITS OF ELEMENTS
ROLEWICZ, S
[J]. STUDIA MATHEMATICA, 1969, 32 (01) : 17 - &
[10] Salas HN, 1999, STUD MATH, V135, P55

← 1 2 →