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arXiv · 1712.01389

On the maximal ideal space of even quasicontinuous functions on the unit circle

Torsten Ehrhardt·Zheng Zhou
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Abstract

Let $PQC$ stand for the set of all piecewise quasicontionus function on the unit circle, i.e., the smallest closed subalgebra of $L^\infty(\mathbb{T})$ which contains the classes of all piecewise continuous function $PC$ and all quasicontinuous functions $QC=(C+H^\infty)\cap(C+\overline{H^\infty})$. We analyze the fibers of the maximal ideal spaces $M(PQC)$ and $M(QC)$ over maximal ideals from $M(\widetilde{QC})$, where $\widetilde{QC}$ stands for the $C^*$-algebra of all even quasicontinous functions. The maximal ideal space $M(\widetilde{QC})$ is decribed and partitioned into various subsets corresponding to different descriptions of the fibers.

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Torsten Ehrhardt, Zheng Zhou. 2017-12-04. On the maximal ideal space of even quasicontinuous functions on the unit circle. https://arxiv.org/abs/1712.01389

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