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

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