대한수학회지 (Journal of the Korean Mathematical Society)

  • 제51권2호
  • /
  • Pages.363-382
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  • 2014
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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HEREDITARILY HYPERCYCLICITY AND SUPERCYCLICITY OF WEIGHTED SHIFTS

  • 투고 : 2013.07.27
  • 심사 : 2013.08.19
  • 발행 : 2014.03.01
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초록

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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참고문헌

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피인용 문헌

  1. Supercyclic translation $C_0$-semigroup on complex sectors vol.36, pp.1, 2016, https://doi.org/10.3934/dcds.2016.36.361
  2. Disjoint supercyclic weighted translations generated by aperiodic elements vol.68, pp.2, 2017, https://doi.org/10.1007/s13348-016-0164-4