## Bulletin of the Belgian Mathematical Society - Simon Stevin

### On the Existence of Transitive and Topologically Mixing Semigroups

José A. Conejero

#### 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

https://projecteuclid.org/euclid.bbms/1190994207

Digital Object Identifier
doi:10.36045/bbms/1190994207

Mathematical Reviews number (MathSciNet)
MR2387043

Zentralblatt MATH identifier
1151.47012

#### 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