HEREDITARILY HYPERCYCLICITY AND SUPERCYCLICITY OF WEIGHTED SHIFTS

Liang, Yu-Xia; Zhou, Ze-Hua

doi:10.4134/JKMS.2014.51.2.363

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HEREDITARILY HYPERCYCLICITY AND SUPERCYCLICITY OF WEIGHTED SHIFTS

Journal title : Journal of the Korean Mathematical Society
Volume 51, Issue 2, 2014, pp.363-382
Publisher : The Korean Mathematical Society
DOI : 10.4134/JKMS.2014.51.2.363

Title & Authors

HEREDITARILY HYPERCYCLICITY AND SUPERCYCLICITY OF WEIGHTED SHIFTS
Liang, Yu-Xia; Zhou, Ze-Hua;

Abstract

In this paper we first characterize the hereditarily hypercyclicity of the unilateral (or bilateral) weighted shifts on the spaces ${$L^2(\mathbb{N},\mathcal{K})$}$ (or ${$L^2(\mathbb{Z},\mathcal{K})$}$ ) with weight sequence { ${$A_n$}$ } of positive invertible diagonal operators on a separable complex Hilbert space ${$\mathcal{K}$}$ . Then we give the necessary and sufficient conditions for the supercyclicity of those weighted shifts, which extends some previous results of H. Salas. At last, we give some conditions for the supercyclicity of three different weighted shifts.

Keywords

hereditarily hypercyclic;supercyclic;weighted shifts;

Language

English

Cited by

2time(s) in CrossRef

Supercyclic translation $C_0$-semigroup on complex sectors, Discrete and Continuous Dynamical Systems, 2015, 36, 1, 361

Disjoint supercyclic weighted translations generated by aperiodic elements, Collectanea Mathematica, 2017, 68, 2, 265

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