华东师范大学学报(自然科学版) ›› 2013, Vol. 2013 ›› Issue (5): 130-135, 143.

• 数学 • 上一篇    下一篇

算子的亚循环性与拓扑一致降标

刘 洋, 曹小红   

  1. 陕西师范大学~~数学与信息科学学院, 西安 710062
  • 收稿日期:2012-11-01 修回日期:2013-02-01 出版日期:2013-09-25 发布日期:2013-09-30

Hypercyclicity and topological uniform descent of bounded linear operators

LIU Yang, CAO Xiao-hong   

  1. Department of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, China
  • Received:2012-11-01 Revised:2013-02-01 Online:2013-09-25 Published:2013-09-30

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摘要： 利用算子的拓扑一致降标,
给出了算子~$A\in\overline{HC(H)}$~的判定方法,
其中~$\overline{HC(H)}$~表示无限维可分的复~Hilbert~空间~$H$~上所有亚循环算子集合的范数闭包.

关键词: 亚循环算子, 拓扑一致降标, 算子的单值延拓性质

Abstract: By using the property of topological uniform descent, this
paper gave the judgement for an operator $A\in\overline{HC(H)}$,
where $\overline{HC(H)}$ denoting the norm-closure of the class of
all the hypercyclic operators on an infinite dimensional separable
complex Hilbert space $H$.

Key words: hypercyclic operator, topological uniform descent, single valued extension property

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