Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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HEREDITARILY HYPERCYCLICITY AND SUPERCYCLICITY OF WEIGHTED SHIFTS

  • Received : 2013.07.27
  • Accepted : 2013.08.19
  • Published : 2014.03.01
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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.

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References

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