HEREDITARILY HYPERCYCLICITY AND SUPERCYCLICITY OF WEIGHTED SHIFTS

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 $\small{L^2(\mathbb{N},\mathcal{K})}$ (or $\small{L^2(\mathbb{Z},\mathcal{K})}$) with weight sequence {$\small{A_n}$} of positive invertible diagonal operators on a separable complex Hilbert space $\small{\mathcal{K}}$. 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
1.
Disjoint supercyclic weighted translations generated by aperiodic elements, Collectanea Mathematica, 2017, 68, 2, 265
2.
Supercyclic translation $C_0$-semigroup on complex sectors, Discrete and Continuous Dynamical Systems, 2015, 36, 1, 361
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