The topological center of the spectrum of some distal algebras

Ali Jabbari Department of Mathematics, University of Kerman

Rings and Algebras mathscidoc:1701.02003

Arkiv for Matematik, 50, (2), 291-304, 2010.3
The topological center of the spectrum of the Weyl algebra$W$, i.e. the norm closure of the algebra generated by the set of functions $\{n\mapsto\lambda^{n^{i}};\lambda\in\mathbb{T}\mbox{ and }i\in\mathbb {N}\}$ , is characterized in a recent paper by$Jabbari$and$Namioka$(Ellis group and the topological center of the flow generated by the map $n\mapsto \lambda^{n^{k}}$ , to appear in$Milan J. Math.$). By the techniques essentially used in the cited paper, the topological center of the spectrum of the subalgebra$W$_{$k$}, the norm closure of the algebra generated by the set of functions $\{n\mapsto\lambda^{n^{i}};\lambda\in\mathbb{T}\mbox{ and }i=0,1,2,\ldots,k\}$ , will be characterized, for all$k$∈ℕ. Also an example of a non-minimal dynamical system, with the enveloping semigroup Σ, for which the set of all continuous elements of Σ is not equal to the topological center of Σ, is given.
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@inproceedings{ali2010the,
  title={The topological center of the spectrum of some distal algebras},
  author={Ali Jabbari},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203632352030019},
  booktitle={Arkiv for Matematik},
  volume={50},
  number={2},
  pages={291-304},
  year={2010},
}
Ali Jabbari. The topological center of the spectrum of some distal algebras. 2010. Vol. 50. In Arkiv for Matematik. pp.291-304. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203632352030019.
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