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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Translation operators on weighted spaces of entire functions
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by Pham Trong Tien PDF
Proc. Amer. Math. Soc. 145 (2017), 805-815 Request permission


We study the dynamical properties of translation operators on both weighted Hilbert and Banach spaces of entire functions. We show that the translation operator on these weighted spaces is always mixing when it is continuous and give necessary and sufficient conditions in terms of weights for the chaos of this operator. We also prove that translation operators can arise as compact perturbations of the identity on weighted Banach spaces.
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Additional Information
  • Pham Trong Tien
  • Affiliation: Hanoi University of Science, Vietnam National University, 334 Nguyen Trai Street, Thanh Xuan, Hanoi, Vietnam
  • MR Author ID: 885842
  • Email:,
  • Received by editor(s): September 14, 2015
  • Received by editor(s) in revised form: April 21, 2016
  • Published electronically: August 23, 2016
  • Additional Notes: This research was partially supported by NAFOSTED under grant No. 101.02-2014.49. This work was completed when the author visited Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank VIASM for its financial support and hospitality.

  • Dedicated: To my supervisor, Professor Alexander V. Abanin, on the occasion of his sixtieth birthday
  • Communicated by: Thomas Schlumprecht
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 805-815
  • MSC (2010): Primary 47B38; Secondary 47A16, 46E15, 46E20
  • DOI:
  • MathSciNet review: 3577879