Disjointness in supercyclicity on the algebra of Hilbert-Schmidt operators
Tóm tắt
In this paper we show that the property of disjoint supercyclic operators T
1, ⋯, T
N
satisfying d-supercyclicity criterion on the same Hilbert space is equivalent to disjointness in supercyclicity of the corresponding left multiplication operators induced by T1, ⋯, T
N
in the strong operator topology. Besides, by the similar discussion, we also obtain that d-hypercyclicity criterion for any T1, ⋯, TN on the same Hilbert space is equivalent to d-hypercyclicity of the corresponding left multiplication operators induced by T1, ⋯, TN in the ‖.‖2 topology.
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