Frequently hypercyclic weighted backward shifts on spaces of real analytic functions

Frequently hypercyclic weighted backward shifts on spaces of real analytic functions

We study frequent hypercyclicity in the case of weighted backward shift operators acting on locally convexspaces of real analytic functions. We obtain certain conditions on frequent hypercyclicity and linear chaoticity of theseoperators using dynamical transference principles and the frequent hypercyclicity criterion.

___

  • [1] Bayart F, Grivaux S. Frequently hypercyclic operators. T Am Math Soc 2006; 358: 5083-5117.
  • [2] Bayart F, Grivaux S. Invariant Gaussian measures for operators on Banach spaces and linear dynamics. P Lond Math Soc 2007; 94: 181-210. [ 3] Bayart F, Matheron E. Dynamics of Linear Operators. Cambridge, UK: Cambridge University Press, 2009.
  • [4] Bayart F, Ruzsa IZ. Difference sets and frequently hypercyclic weighted shifts. Ergodic Theory Dynam Systems 2015; 35: 691-709.
  • [5] Bonet J. Hypercyclic and chaotic convolution operators. J Lond Math Soc 2000; 62: 253-262.
  • [6] Bonilla A, Grosse-Erdmann KG. Frequent hypercyclic operators and vectors. Ergodic Theory Dynam Systems 2007; 27: 383-404.
  • [7] Domański P. Notes on real analytic functions and classical operators. In: Topics in Complex Analysis and Operator Theory, Winter School in Complex Analysis and Operator Theory; February 2010; Valencia, Spain. Providence, RI, USA: AMS, 2012, pp. 3-47.
  • [8] Domański P, Karıksız CD. Eigenvalues and dynamical properties of weighted backward shifts on the space of real analytic functions. Studia Math 2018; 242: 57-78.
  • [9] Domański P, Vogt D. The space of real analytic functions has no basis. Studia Math 2000; 142: 187-200.
  • [10] Grosse-Erdmann KG, Peris A. Linear Chaos. Berlin, Germany: Springer, 2011.
  • [11] Junde W, Ronglu L. Unconditional convergent series on locally convex spaces. Taiwanese J Math 2000; 4: 253-259.
  • [12] Meise R, Vogt D. Introduction to Functional Analysis. Oxford, UK: Clarendon Press, 1997.
  • [13] Menet Q. Linear chaos and frequent hypercyclicity. Trans Amer Math Soc 2017; 369: 4977-4994.
  • [14] Rolewicz S. On orbits of elements. Studia Math 1969; 32: 17-22.