Invertibility Criteria in C -algebras of Functional Operators with Shifts and PQC Coefficients

Maria Amélia Bastos, C. A. Fernandes, Yu I. Karlovich

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1 Citation (Scopus)

Abstract

Let G be an amenable discrete group of orientation-preserving piecewise smooth homeomorphisms g: T→ T, with finite sets of discontinuities for their derivatives g , which acts topologically freely on T\ Λ , where Λ is the interior of a nonempty closed set Λ ⊂ T composed by all common fixed points for all shifts g∈ G. Invertibility criteria are established for the operators in the C -algebra A:=alg(PQC,UG)⊂B(L2(T))generated by all functional operators of the form ∑ g F a g U g , where a g I are multiplication operators by piecewise quasicontinuous functions a g ∈ PQC on T, Ug:φ↦|g′|1/2(φ∘g) are unitary weighted shift operators on L 2 (T) , and F is any finite subset of the group G.

Original languageEnglish
Article number19
JournalIntegral Equations And Operator Theory
Volume91
Issue number3
DOIs
Publication statusPublished - 1 Jun 2019

Keywords

  • Amenable group
  • C -algebra
  • Functional operator
  • Invertibility
  • Piecewise quasicontinuous function
  • Shift

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