Banach Journal of Mathematical Analysis

Disjoint hypercyclic weighted pseudoshift operators generated by different shifts

Ya Wang, Cui Chen, and Ze-Hua Zhou

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Let I be a countably infinite index set, and let X be a Banach sequence space over I. In this article, we characterize the disjoint hypercyclic and supercyclic weighted pseudoshift operators on X in terms of the weights, the OP-basis, and the shift mappings on I. Also, the shifts on weighted Lp spaces of a directed tree and the operator weighted shifts on 2(Z,K) are investigated as special cases.

Article information

Banach J. Math. Anal., Volume 13, Number 4 (2019), 815-836.

Received: 6 April 2018
Accepted: 12 November 2018
First available in Project Euclid: 9 October 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A16: Cyclic vectors, hypercyclic and chaotic operators
Secondary: 47B38: Operators on function spaces (general) 46E15: Banach spaces of continuous, differentiable or analytic functions

disjoint hypercyclic disjoint supercyclic weighted pseudoshifts operator weighted shifts Banach space


Wang, Ya; Chen, Cui; Zhou, Ze-Hua. Disjoint hypercyclic weighted pseudoshift operators generated by different shifts. Banach J. Math. Anal. 13 (2019), no. 4, 815--836. doi:10.1215/17358787-2018-0039.

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  • [1] F. Bayart and É. Matheron, Dynamics of Linear Operators, Cambridge Tracts in Math. 179, Cambridge Univ. Press, Cambridge, 2009.
  • [2] L. Bernal-González, Disjoint hypercyclic operators, Studia Math. 182 (2007), no. 2, 113–131.
  • [3] J. Bès, Ö. Martin, and A. Peris, Disjoint hypercyclic linear fractional composition operators, J. Math. Anal. Appl. 381 (2011), no. 2, 843–856.
  • [4] J. Bès, Ö. Martin, A. Peris, and S. Shkarin, Disjoint mixing operators, J. Funct. Anal. 263 (2012), no. 5, 1283–1322.
  • [5] J. Bès, Ö. Martin, and R. Sanders, Weighted shifts and disjoint hypercyclicity, J. Operator Theory 72 (2014), no. 1, 15–40.
  • [6] J. Bès and A. Peris, Disjointness in hypercyclicity, J. Math. Anal. Appl. 336 (2007), no. 1, 297–315.
  • [7] C. C. Chen, Disjoint hypercyclic weighted translations on groups, Banach J. Math. Anal. 11 (2017), no. 3, 459–476.
  • [8] N. S. Feldman, Hypercyclicity and supercyclicity for invertible bilateral weighted shifts, Proc. Amer. Math. Soc. 131 (2003), no. 2, 479–485.
  • [9] K.-G. Grosse-Erdmann, Hypercyclic and chaotic weighted shifts, Studia Math. 139 (2000), no. 1, 47–68.
  • [10] K.-G. Grosse-Erdmann and A. Peris Manguillot, Linear Chaos, Universitext, Springer, London, 2011.
  • [11] M. Hazarika and S. C. Arora, Hypercyclic operator weighted shifts, Bull. Korean Math. Soc. 41 (2004), no. 4, 589–598.
  • [12] Z. J. Jabłoński, I. B. Jung, and J. Stochel, Weighted shifts on directed trees, Mem. Amer. Math. Soc. 216 (2009), no. 1017.
  • [13] Y. X. Liang and Z. H. Zhou, Disjoint supercyclic powers of weighted shifts on weighted sequence spaces, Turkish J. Math. 38 (2014), no. 6, 1007–1022.
  • [14] Y. X. Liang and Z. H. Zhou, Hereditarily hypercyclicity and supercyclicity of weighted shifts, J. Korean Math. Soc. 51 (2014), no. 2, 363–382.
  • [15] Ö. Martin, Disjoint hypercyclic and supercyclic composition operators, Ph.D. dissertation, Bowling Green State University, Bowling Green, OH, 2011.
  • [16] R. A. Martínez-Avendaño, Hypercyclicity of shifts on weighted $L^{p}$ spaces of directed trees, J. Math. Anal. Appl. 446 (2017), no. 1, 823–842.
  • [17] H. N. Salas, Hypercyclic weighted shifts, Trans. Amer. Math. Soc. 347 (1995), no. 3, 993–1004.
  • [18] H. N. Salas, Supercyclicity and weighted shifts, Studia Math. 135 (1999), no. 1, 55–74.
  • [19] H. N. Salas, Dual disjoint hypercyclic operators, J. Math. Anal. Appl. 374 (2011), no. 1, 106–117.
  • [20] S. Shkarin, A short proof of existence of disjoint hypercyclic operators, J. Math. Anal. Appl. 367 (2010), no. 2, 713–715.
  • [21] Y. Wang and Z. H. Zhou, Disjoint hypercyclic powers of weighted pseudo-shifts, Bull. Malays. Math. Sci. Soc., published online 29 November 2017.
  • [22] Y. Wang and Z. H. Zhou, Disjoint hypercyclic weighted pseudo-shifts on Banach sequence spaces, Collect. Math. 69 (2018), no. 3, 437–449.
  • [23] L. Zhang, H. Q. Lu, X. M. Fu, and Z. H. Zhou, Disjoint hypercyclic powers of weighted translations on groups, Czechoslovak Math. J. 67(142) (2017), no. 3, 839–853.
  • [24] L. Zhang and Z. H. Zhou, Disjointness in supercyclicity on the algebra of Hilbert-Schmidt operators, Indian J. Pure Appl. Math. 46 (2015), no. 2, 219–228.