Journal of Integrative Natural Science (통합자연과학논문집)

The Basic Science Institute Chosun University (조선대학교 기초과학연구원)
권호 표지
DOI QR코드

DOI QR Code

𝓐-Frequent Hypercyclicity in an Algebra of Operators

  • Ahn, Ka Kyung (College of Humanities and General Education, Soekyeong University)
  • Received : 2017.05.08
  • Accepted : 2017.06.25
  • Published : 2017.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

We study a notion of $\mathcal{A}$-frequent hypercyclicity of linear maps between the Banach algebras consisting of operators on a separable infinite dimensional Banach space. We prove a sufficient condition for a linear map to satisfy the $\mathcal{A}$-frequent hypercyclicity in the strong operator topology.

Keywords

Acknowledgement

Supported by : Seokyeong University

References

  1. M. Gupta and A. Mundayadan, "q-frequently hypercyclic operators", Banach Journal of Mathematical Analysis, Vol. 9, pp. 114-126, 2015.
  2. F. Bayart and E. Matheron, "(Non-)weakly mixing operators and hypercyclicity sets", Annales de L'institut Fourier, Vol. 59, pp. 1-35, 2009. https://doi.org/10.5802/aif.2425
  3. J. Bes, Q. Menet, A. Peris, and Y. Puig, "Recurrence properties of hypercyclic operators", Mathematische Annalen, Vol. 366, pp. 545-572, 2016. https://doi.org/10.1007/s00208-015-1336-3
  4. K. C. Chan and R. D. Taylor, "Hypercyclic subspaces of a banach space", Integral Equations and Operator Theory, Vol. 41, pp. 381-388, 2001. https://doi.org/10.1007/BF01202099
  5. Q. Menet, "Existence and non-existence of frequently hypercyclic subspaces for weighted shifts", Proc. Am. Math. Soc., Vol. 143, pp. 2469-2477, 2015. https://doi.org/10.1090/S0002-9939-2015-12444-6