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

Let $PQC$ stand for the set of all piecewise quasicontionus function on the unit circle, i.e., the smallest closed subalgebra of $L^{\mathrm{\infty }}(\mathbb{T})$ which contains the classes of all piecewise continuous function $PC$ and all quasicontinuous functions $QC=(C+H^{\mathrm{\infty }})\cap (C+\overline{H^{\mathrm{\infty }}})$. 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 $C^{\ast }$-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.