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

Abstract

Let PQC stand for the set of all piecewise quasicontinuous functions on the unit circle, i.e., the smallest closed subalgebra of $L^{\infty}\,(\mathbb{T})$ which contains the classes of all piecewise continuous functions 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 quasicontinuous functions. The maximal ideal space $M(\widetilde{QC})$ is described and partitioned into various subsets corresponding to different descriptions of the fibers.

Dedicated to Marinus A. Kaashoek on the occasion of his eightieth birthday.