HYPERCYCLIC OPERATORS ON QUASI-MAZUR SPACES  

作　　者：丘京辉 

机构地区：[1]Department of Mathematics,Suzhou University

出　　处：《Acta Mathematica Scientia》2010年第5期1709-1720,共12页数学物理学报（B辑英文版）

基　　金：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, KSthe （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.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, KSthe （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 Kothe （LF）-sequence space 

分 类 号：O177[理学—数学]