Banach Journal of Mathematical Analysis

Disjoint hypercyclic weighted translations on groups

Chung-Chuan Chen

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Abstract

Let 1p<, and let G be a locally compact group. We characterize disjoint hypercyclic weighted translation operators on the Lebesgue space Lp(G) in terms of the weight, the Haar measure, and the group element. Disjoint supercyclic, disjoint mixing, and dual disjoint hypercyclic weighted translation operators are also characterized.

Article information

Source
Banach J. Math. Anal., Volume 11, Number 3 (2017), 459-476.

Dates
Received: 23 February 2016
Accepted: 21 July 2016
First available in Project Euclid: 19 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1492618124

Digital Object Identifier
doi:10.1215/17358787-2017-0001

Mathematical Reviews number (MathSciNet)
MR3679891

Zentralblatt MATH identifier
06754298

Subjects
Primary: 47A16: Cyclic vectors, hypercyclic and chaotic operators
Secondary: 47B38: Operators on function spaces (general) 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc.

Keywords
disjoint hypercyclicity topological transitivity locally compact group $L^{p}$-space

Citation

Chen, Chung-Chuan. Disjoint hypercyclic weighted translations on groups. Banach J. Math. Anal. 11 (2017), no. 3, 459--476. doi:10.1215/17358787-2017-0001. https://projecteuclid.org/euclid.bjma/1492618124


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References

  • [1] L. Bernal-González, Disjoint hypercyclic operators, Studia Math. 182 (2007), no. 2, 113–131.
  • [2] J. Bès, Ö. Martin, and A. Peris, Disjoint hypercyclic linear fractional composition operators, J. Math. Anal. Appl. 381 (2011), no. 2, 843–856.
  • [3] J. Bès, Ö. Martin, A. Peris, and S. Shkarin, Disjoint mixing operators, J. Funct. Anal. 263 (2012), no. 5, 1283–1322.
  • [4] J. Bès, Ö. Martin, and R. Sanders, Weighted shifts and disjoint hypercyclicity, J. Operator Theory 72 (2014), no. 1, 15–40.
  • [5] J. Bès and A. Peris, Disjointness in hypercyclicity, J. Math. Anal. Appl. 336 (2007), no. 1, 297–315.
  • [6] C.-C. Chen, Chaotic weighted translations on groups, Arch. Math. 97 (2011), no. 1, 61–68.
  • [7] C.-C. Chen, Supercyclic and Cesàro hypercyclic weighted translations on groups, Taiwanese J. Math. 16 (2012), no. 5, 1815–1827.
  • [8] C.-C. Chen, Hypercyclic weighted translations generated by non-torsion elements, Arch. Math. 101 (2013), no. 2, 135–141.
  • [9] C.-C. Chen and C.-H. Chu, Hypercyclic weighted translations on groups, Proc. Amer. Math. Soc. 139 (2011), no. 8, 2839–2846.
  • [10] G. Costakis and M. Sambarino, Topologically mixing hypercyclic operators, Proc. Amer. Math. Soc. 132 (2004), no. 2, 385–389.
  • [11] K.-G. Grosse-Erdmann, Universal families and hypercyclic operators, Bull. Amer. Math. Soc. (N.S.) 36 (1999), no. 3, 345–381.
  • [12] K.-G. Grosse-Erdmann, Hypercyclic and chaotic weighted shifts, Studia Math. 139 (2000), no. 1, 47–68.
  • [13] F. León-Saavedra, Operators with hypercyclic Cesàro means, Studia Math. 152 (2002), no. 3, 201–215.
  • [14] Ö. Martin, Disjoint hypercyclic and supercyclic composition operators, Ph.D. dissertation, Bowling Green State University, Bowling Green, Ohio, 2010.
  • [15] H. Salas, A hypercyclic operator whose adjoint is also hypercyclic, Proc. Amer. Math. Soc. 112 (1991), no. 3, 765–770.
  • [16] H. Salas, Hypercyclic weighted shifts, Trans. Amer. Math. Soc. 347 (1995), no. 1, 993–1004.
  • [17] H. Salas, Dual disjoint hypercyclic operators, J. Math. Anal. Appl. 374 (2011), no. 1, 106–117.
  • [18] S. Shkarin, A short proof of existence of disjoint hypercyclic operaors, J. Math. Anal. Appl. 367 (2010), no. 2, 713–715.