HYPERCYCLIC OPERATORS ON QUASI-MAZUR SPACES

doi:10.1016/S0252-9602(10)60164-6

Abstract

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

CLC Number:

47A16

QIU Jing-Hui. HYPERCYCLIC OPERATORS ON QUASI-MAZUR SPACES[J].Acta mathematica scientia,Series B, 2010, 30(5): 1709-1720.

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