数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (5): 1709-1720.doi: 10.1016/S0252-9602(10)60164-6

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HYPERCYCLIC OPERATORS ON QUASI-MAZUR SPACES

丘京辉   

  1. Department of Mathematics, Suzhou University, Suzhou 215006, China
  • 收稿日期:2007-11-01 出版日期:2010-09-20 发布日期:2010-09-20
  • 基金资助:

    Supported by the National Natural Science Foundation of China (10571035, 10871141).

HYPERCYCLIC OPERATORS ON QUASI-MAZUR SPACES

 QIU Jing-Hui   

  1. Department of Mathematics, Suzhou University, Suzhou 215006, China
  • Received:2007-11-01 Online:2010-09-20 Published:2010-09-20
  • Supported by:

    Supported by the National Natural Science Foundation of China (10571035, 10871141).

摘要:

Modifying the method of Ansari, we give some criteria for hypercyclicity of quasi-Mazur spaces. They can be applied to judging hypercyclicity of non-complete and non-metrizable locally convex spaces. For some special locally convex spaces, for example, K\"{o}the (LF)-sequence spaces and countable inductive limits of quasi-Mazur spaces, we investigate their hypercyclicity. As we see, bounded biorthogonal systems play an important role in the construction of Ansari. Moreover, we obtain characteristic conditions respectively for locally convex spaces having  bounded sequences with dense linear spans and for locally convex spaces  having bounded absorbing sets, which are useful in judging the existence of bounded biorthogonal systems.

关键词: hypercyclic operator, bounded biorthogonal systems,  quasi-Mazur space, inductive limit, K\"{o}the (LF)-sequence space

Abstract:

Modifying the method of Ansari, we give some criteria for hypercyclicity of quasi-Mazur spaces. They can be applied to judging hypercyclicity of non-complete and non-metrizable locally convex spaces. For some special locally convex spaces, for example, K\"{o}the (LF)-sequence spaces and countable inductive limits of quasi-Mazur spaces, we investigate their hypercyclicity. As we see, bounded biorthogonal systems play an important role in the construction of Ansari. Moreover, we obtain characteristic conditions respectively for locally convex spaces having  bounded sequences with dense linear spans and for locally convex spaces  having bounded absorbing sets, which are useful in judging the existence of bounded biorthogonal systems.

Key words: hypercyclic operator, bounded biorthogonal systems,  quasi-Mazur space, inductive limit, K\"{o}the (LF)-sequence space

中图分类号: 

  • 47A16