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.
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References
T. Bermüdez, A. Bonilla and A. Peris, On hypercyclicity and supercyclicity criteria, Bull. Aust. Math. Soc., 70 (2004), 45–54.
L. Bernal-Gonzâlez, Disjoint hypercyclic operators, Studia Math., 182 (2007), 113–131.
L. Bernai and K. G. Grosse-Erdmann, The hypercyclicity criterion for sequences of operators, Studia Math., 157 (2003), 17–32.
F. Bayart and E. Matheron, Dynamics of Linear Operators, Cambridge University Press, Cambridge, 2009.
J. Bonet, F. Martnez-Gimnez and A. Peris, Universal and chaotic multipliers on spaces of operators, J. Math. Anal. Appl., 297 (2004), 599–611.
J. Bès, Ö. Martin and A. Peris, Disjoint hypercyclic linear fractional composition operators, J. Math. Anal. Appl., 381 (2011), 843–856.
J. Bès, Ö. Martin, A. Peris and S. Shkarin, Disjoint mixing operators, J. Funct. Anal., 263 (2012), 1283–1322.
J. Bès and A. Peris, Hereditarily hypercyclic operators, J. Funct. Anal., 167 (1999), 94–112.
J. Bès and A. Peris, Disjointness in hypercyclicity, J. Math. Anal. Appl., 336 (2007), 297–315.
N. Feldman, Hypercyclicity and Supercyclicity for invertible bilateral weighted shifts, Proc. Amer. Math. Soc., 131(2)(2003), 479–485.
K. G. Grosse-Erdmann and A. Peris Manguillot, Linear Chaos, Universitext. Springer, London, 2011.
H. M. Hilden and L. J. Wallen, Some cyclic and non-cyclic vectors of certain operators, Ind. Univ. Math. J., 23 (1974), 557–565.
F. Martmez-Giménez and A. Peris, Universality and chaos for tensor products of operators, J. Approx. Theory, 124 (2003), 7–24.
H. N. Salas, Hypercyclic weighted shifts, Trans. Amer. Math. Soc., 347 (1995), 993–1004.
H. N. Salas, Supercyclicity and weighted shifts, Studia Math., 135(1)(1999), 55–74.
B. Yousefi and H. Rezaei, Hypercyclicity on the algebra of Hilbert-Schmidt operators, Result. Math., 46 (2004), 174–180.
B. Yousefi and H. Rezaei, Supercyclicity in the operator algebra using Hilbert-Schmidt operators, Rendiconti del Circolo Matematico di Palermo. Serie H., Tomo LVI (2007), 33–42.
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The authors were supported in part by the National Natural Science Foundation of China (Grant Nos. 11371276; 11301373; 11201331) and by Natural Science Foundation of Hebei Province (Grant No. A2013202265).
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Zhang, L., Zhou, ZH. Disjointness in supercyclicity on the algebra of Hilbert-Schmidt operators. Indian J Pure Appl Math 46, 219–228 (2015). https://doi.org/10.1007/s13226-015-0116-9
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DOI: https://doi.org/10.1007/s13226-015-0116-9