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

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

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.

Keywords

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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