Functiones et Approximatio Commentarii Mathematici

A hypercyclicity criterion for non-metrizable topological vector spaces

Alfred Peris

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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.

Article information

Source
Funct. Approx. Comment. Math., Volume 59, Number 2 (2018), 279-284.

Dates
First available in Project Euclid: 26 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.facm/1529978433

Digital Object Identifier
doi:10.7169/facm/1739

Mathematical Reviews number (MathSciNet)
MR3892306

Zentralblatt MATH identifier
07055556

Subjects
Primary: 47A16: Cyclic vectors, hypercyclic and chaotic operators 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)

Keywords
hypercyclic operators

Citation

Peris, Alfred. A hypercyclicity criterion for non-metrizable topological vector spaces. Funct. Approx. Comment. Math. 59 (2018), no. 2, 279--284. doi:10.7169/facm/1739. https://projecteuclid.org/euclid.facm/1529978433


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Adam Mickiewicz University, Faculty of Mathematics and Computer Science

Functiones et Approximatio Commentarii Mathematici

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