Densely hereditarily hypercyclic sequences and large hypercyclic manifolds

被引：35

作者：

Bernal-González, L ^{[1
]}

机构：

[1] Univ Sevilla, Fac Matemat, Dept Anal Matemat, E-41080 Seville, Spain

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1999年 / 127卷 / 11期

关键词：

hypercyclic vector; linear operator; densely hereditarily hypercyclic sequence; infinite-dimensional manifold; dense manifold; metrizable topological vector space; entire function of subexponential type; Runge domain; infinite order linear differential operator;

D O I：

10.1090/S0002-9939-99-05185-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove in this paper that if (T-n) is a hereditarily hypercyclic sequence of continuous linear mappings between two topological vector spaces X and Y, where Y is metrizable, then there is an infinite-dimensional linear submanifold M of X such that each non-zero vector of M is hypercyclic for (T-n). If, in addition, X is metrizable and separable and (T-n) is densely hereditarily hypercyclic, then M can be chosen dense.

引用

页码：3279 / 3285

页数：7

共 18 条

[1] HYPERCYCLIC AND CYCLIC VECTORS
ANSARI, SI
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1995, 128 (02) : 374 - 383
[2] Existence of hypercyclic operators on topological vector spaces
Ansari, SI
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1997, 148 (02) : 384 - 390
[3] BERNALGONZALEZ L, IN PRESS P AM MATH S
[4] BERNALGONZALEZ L, IN PRESS J APPROX TH
[5] BESS J, IN PRESS P AM MATH S
[6] BONET J, IN PRESS J FUNCT ANA
[7] Bourdon P. S., 1997, MEMOIRS AM MATH SOC, V596
[8] INVARIANT-MANIFOLDS OF HYPERCYCLIC VECTORS
BOURDON, PS
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 118 (03) : 845 - 847
[9] UNIVERSAL VECTORS FOR OPERATORS ON SPACES OF HOLOMORPHIC-FUNCTIONS
GETHNER, RM
SHAPIRO, JH
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 100 (02) : 281 - 288
[10] OPERATORS WITH DENSE, INVARIANT, CYCLIC VECTOR MANIFOLDS
GODEFROY, G
SHAPIRO, JH
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1991, 98 (02) : 229 - 269

← 1 2 →