HEREDITARILY HYPERCYCLICITY AND SUPERCYCLICITY OF WEIGHTED SHIFTS
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In this paper we first characterize the hereditarily hyper- cyclicity of the unilateral (or bilateral) weighted shifts on the spaces L² (N,K) (or L²(Z,K)) with weight sequence {An} of positive invert- ible diagonal operators on a separable complex Hilbert space 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.
Abstract
In this paper we first characterize the hereditarily hyper- cyclicity of the unilateral (or bilateral) weighted shifts on the spaces L² (N,K) (or L²(Z,K)) with weight sequence {An} of positive invert- ible diagonal operators on a separable complex Hilbert space 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.
참고문헌 (12)
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