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

  • Torsten EhrhardtEmail author
  • Zheng Zhou
Part of the Operator Theory: Advances and Applications book series (OT, volume 271)


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.


quasicontinuous function piecewise quasicontinuous function maximal ideal space 

Mathematics Subject Classification (2010)

Primary 46J10 Secondary 46J20 47B35 


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaSanta CruzUSA

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