Some remarks on distributional chaos for bounded linear operators

Authors : Lvlin LUO, Bingzhe HOU

Pages : 251-258

Doi:10.3906/mat-1403-41

View : 8 | Download : 5

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :The aim of this paper is to study distributional chaos for bounded linear operators. We show that distributional chaos of type k \in {1,2} is an invariant of topological conjugacy between two bounded linear operators. We give a necessary condition for distributional chaos of type 2 where it is possible to distinguish distributional chaos and Li--Yorke chaos. Following this condition, we compare distributional chaos with other well-studied notions of chaos for backward weighted shift operators and give an alternative proof to the one where strong mixing does not imply distributional chaos of type 2 insert ignore into journalissuearticles values(Martínez-Giménez F, Oprocha P, Peris A. Distributional chaos for operators with full scrambled sets. Math Z 2013; 274: 603--612.);. Moreover, we also prove that there exists an invertible bilateral forward weighted shift operator such that it is DC1 but its inverse is not DC2.
Keywords : Distributional chaos, operators, weighted shifts, topological conjugacy, strong mixing