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march 2018 Dynamics of linear operators on non-Archimedean vector spaces
Farrukh Mukhamedov, Otabek Khakimov
Bull. Belg. Math. Soc. Simon Stevin 25(1): 85-105 (march 2018). DOI: 10.36045/bbms/1523412055

Abstract

In the present paper we study dynamics of linear operators defined on topological vector space over non-Archimedean valued fields. We give sufficient and necessary conditions of hypercyclicity (resp. supercyclicity) of linear operators on separable $F$-spaces. It is proven that a linear operator $T$ on topological vector space $X$ is hypercyclic (supercyclic) if it satisfies Hypercyclicity (resp. Supercyclicity) Criterion. We consider backward shifts on $c_0(\bz)$ and $c_0(\bn)$, respectively, and characterize hypercyclicity and supercyclicity of such kinds of shifts. Finally, we study hypercyclicity, supercyclicity of operators $\lambda I+\mu B$, where $I$ is identity and $B$ is backward shift. We note that there are essential differences between the non-Archimedean and real cases.

Citation

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Farrukh Mukhamedov. Otabek Khakimov. "Dynamics of linear operators on non-Archimedean vector spaces." Bull. Belg. Math. Soc. Simon Stevin 25 (1) 85 - 105, march 2018. https://doi.org/10.36045/bbms/1523412055

Information

Published: march 2018
First available in Project Euclid: 11 April 2018

zbMATH: 06882544
MathSciNet: MR3784508
Digital Object Identifier: 10.36045/bbms/1523412055

Subjects:
Primary: 37A25, 47A16, 47S10

Rights: Copyright © 2018 The Belgian Mathematical Society

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Vol.25 • No. 1 • march 2018
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