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October 2012 The topological center of the spectrum of some distal algebras
Ali Jabbari
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Ark. Mat. 50(2): 291-304 (October 2012). DOI: 10.1007/s11512-010-0132-2

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.

Funding Statement

A grant from Mahani Mathematical Research Center is gratefully acknowledged.

Citation

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Ali Jabbari. "The topological center of the spectrum of some distal algebras." Ark. Mat. 50 (2) 291 - 304, October 2012. https://doi.org/10.1007/s11512-010-0132-2

Information

Received: 11 March 2010; Published: October 2012
First available in Project Euclid: 31 January 2017

zbMATH: 1277.43009
MathSciNet: MR2961324
Digital Object Identifier: 10.1007/s11512-010-0132-2

Rights: 2010 © Institut Mittag-Leffler

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Vol.50 • No. 2 • October 2012
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