Disjointness in supercyclicity on the algebra of Hilbert-Schmidt operators

Liang Zhang () and Ze-Hua Zhou ()
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Liang Zhang: Tianjin University
Ze-Hua Zhou: Tianjin University

Indian Journal of Pure and Applied Mathematics, 2015, vol. 46, issue 2, 219-228

Abstract: Abstract 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.

Keywords: Disjoint supercyclic; left multiplication operators; Hilbert-Schmidt operators (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s13226-015-0116-9

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