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Disjointness in supercyclicity on the algebra of Hilbert-Schmidt operators

Author

Listed:
  • Liang Zhang

    (Tianjin University)

  • Ze-Hua Zhou

    (Tianjin University)

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.

Suggested Citation

  • Liang Zhang & Ze-Hua Zhou, 2015. "Disjointness in supercyclicity on the algebra of Hilbert-Schmidt operators," Indian Journal of Pure and Applied Mathematics, Springer, vol. 46(2), pages 219-228, April.
    • Handle: RePEc:spr:indpam:v:46:y:2015:i:2:d:10.1007_s13226-015-0116-9
    DOI: 10.1007/s13226-015-0116-9
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