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December 2018 A hypercyclicity criterion for non-metrizable topological vector spaces
Alfred Peris
Funct. Approx. Comment. Math. 59(2): 279-284 (December 2018). DOI: 10.7169/facm/1739

Abstract

We provide a sufficient condition for an operator $T$ on a non-metrizable and sequentially separable topological vector space $X$ to be sequentially hypercyclic. This condition is applied to some particular examples, namely, a composition operator on the space of real analytic functions on $]0,1[$, which solves two problems of Bonet and Doma\'nski [3], and the ``snake shift'' constructed in [5] on direct sums of sequence spaces. The two examples have in common that they do not admit a densely embedded F-space $Y$ for which the operator restricted to $Y$ is continuous and hypercyclic, i.e., the hypercyclicity of these operators cannot be a consequence of the comparison principle with hypercyclic operators on F-spaces.

Citation

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Alfred Peris. "A hypercyclicity criterion for non-metrizable topological vector spaces." Funct. Approx. Comment. Math. 59 (2) 279 - 284, December 2018. https://doi.org/10.7169/facm/1739

Information

Published: December 2018
First available in Project Euclid: 26 June 2018

zbMATH: 07055556
MathSciNet: MR3892306
Digital Object Identifier: 10.7169/facm/1739

Subjects:
Primary: 47A16 , 47B37

Keywords: Hypercyclic operators

Rights: Copyright © 2018 Adam Mickiewicz University

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Vol.59 • No. 2 • December 2018
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