## Arkiv för Matematik

• Ark. Mat.
• Volume 50, Number 2 (2012), 291-304.

### The topological center of the spectrum of some distal algebras

Ali Jabbari

#### Abstract

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 Wk, 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.

#### Note

A grant from Mahani Mathematical Research Center is gratefully acknowledged.

#### Article information

Source
Ark. Mat., Volume 50, Number 2 (2012), 291-304.

Dates
Received: 11 March 2010
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907171

Digital Object Identifier
doi:10.1007/s11512-010-0132-2

Mathematical Reviews number (MathSciNet)
MR2961324

Zentralblatt MATH identifier
1277.43009

Rights
2010 © Institut Mittag-Leffler

#### Citation

Jabbari, Ali. The topological center of the spectrum of some distal algebras. Ark. Mat. 50 (2012), no. 2, 291--304. doi:10.1007/s11512-010-0132-2. https://projecteuclid.org/euclid.afm/1485907171

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