## 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 language | English |
---|---|

Article number | 19 |

Journal | Integral Equations And Operator Theory |

Volume | 91 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jun 2019 |

## Keywords

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