## Abstract

The C^{∗}-algebra B of bounded linear operators on the space L^{2}}T, which is generated by all multiplication operators by piecewise quasicontinuous functions, by the Cauchy singular integral operator and by the range of a unitary representation of a group G of orientation-preserving diffeomorphisms of T onto itself that have the same finite set of fixed points for all (Formula presented), is studied. A Fredholm symbol calculus for the C^{∗}-algebra B and a Fredholm criterion for the operators (Formula presented) are established by using spectral measures and the local-trajectory method for studying C^{∗}-algebras associated with C^{∗}-dynamical systems.

Original language | English |
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Title of host publication | Operator Theory: Advances and Applications |

Publisher | Springer International Publishing Switzerland |

Pages | 25-64 |

Number of pages | 40 |

DOIs | |

Publication status | Published - 1 Jan 2018 |

### Publication series

Name | Operator Theory: Advances and Applications |
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Publisher | Springer International Publishing Switzerland |

Volume | 267 |

ISSN (Print) | 0255-0156 |

ISSN (Electronic) | 2296-4878 |

## Keywords

- Amenable group
- C-algebra
- Fredholmness
- Local-trajectory method
- Piecewise quasicontinuous function
- Representation of a C-algebra
- Singular integral operator with shifts
- Spectral measure
- Symbol calculus

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