Abstract
In Jabbari and Namioka (Milan J. Math. 78:503–522, 2010), the authors characterized the spectrum M(W) of the Weyl algebra W, i.e. the norm closure of the algebra generated by the family of functions \(\{n\mapsto x^{n^{k}}; x\in\mathbb{T}, k\in\mathbb{N}\}\), (\(\mathbb{T}\) the unit circle), with a closed subgroup of \(E(\mathbb{T})^{\mathbb{N}}\) where \(E(\mathbb{T})\) denotes the family of the endomorphisms of the multiplicative group \(\mathbb{T}\). But the size of M(W) in \(E(\mathbb{T})^{\mathbb{N}}\) as well as the induced group operation were left as a problem. In this paper, we will give a solution to this problem.
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Acknowledgements
The author would like to thank Professor Isaac Namioka for reading the paper carefully and also for his fruitful suggestions. Also the very helpful suggestions of the kind referee are acknowledged.
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Communicated by Mike Mislove.
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Jabbari, A. On a problem concerning the Banach algebra generated by the maps \(n\mapsto\lambda^{\binom{n}{k}}\) . Semigroup Forum 85, 160–168 (2012). https://doi.org/10.1007/s00233-012-9412-4
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DOI: https://doi.org/10.1007/s00233-012-9412-4