Bulletin of the Belgian Mathematical Society - Simon Stevin

On the Existence of Transitive and Topologically Mixing Semigroups

José A. Conejero

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Abstract

We prove in this note that every separable infinite dimensional complex Fréchet space different from $\omega$, the countably infinite product of lines, admits a topologically mixing analytic uniformly continuous semigroup of operators. The study of the existence of transitive semigroups on $\omega$, and on its predual $\varphi$ is also considered.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 14, Number 3 (2007), 463-471.

Dates
First available in Project Euclid: 28 September 2007

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1190994207

Digital Object Identifier
doi:10.36045/bbms/1190994207

Mathematical Reviews number (MathSciNet)
MR2387043

Zentralblatt MATH identifier
1151.47012

Subjects
Primary: 47A16: Cyclic vectors, hypercyclic and chaotic operators
Secondary: 47D03: Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20}

Keywords
Transitive Semigroup Hypercyclic Semigroup Topologically Mixing Semigroup Analytic Semigroup

Citation

Conejero, José A. On the Existence of Transitive and Topologically Mixing Semigroups. Bull. Belg. Math. Soc. Simon Stevin 14 (2007), no. 3, 463--471. doi:10.36045/bbms/1190994207. https://projecteuclid.org/euclid.bbms/1190994207


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