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Translation operators on weighted spaces of entire functions


Author: Pham Trong Tien
Journal: Proc. Amer. Math. Soc. 145 (2017), 805-815
MSC (2010): Primary 47B38; Secondary 47A16, 46E15, 46E20
DOI: https://doi.org/10.1090/proc/13254
Published electronically: August 23, 2016
MathSciNet review: 3577879
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Abstract: 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
Email: phamtien@mail.ru, phamtien@vnu.edu.vn

DOI: https://doi.org/10.1090/proc/13254
Keywords: Weighted spaces of entire functions, translation operator, hypercyclic operator, mixing operator, chaotic operator
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
Article copyright: © Copyright 2016 American Mathematical Society