## Abstract

It is proved that the Wiener algebra of functions on a connected compact abelian group whose Bohr-Fourier spectra are contained in a fixed subsemigroup of the (additive) dual group, is projective free. The semigroup is assumed to contain zero and have the property that it does not contain both a nonzero element and its opposite. The projective free property is proved also for the algebra of continuous functions with the same condition on their Bohr-Fourier spectra. As an application, the connected components of the set of factorable matrices are described. The proofs are based on a key result on homotopies of continuous maps on the maximal ideal spaces of the algebras under consideration.

Original language | English (US) |
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Pages (from-to) | 918-932 |

Number of pages | 15 |

Journal | Journal of Functional Analysis |

Volume | 259 |

Issue number | 4 |

DOIs | |

State | Published - Aug 2010 |

## Keywords

- Compact abelian group
- Factorization of Wiener-Hopf type
- Projective free
- Wiener algebra

## ASJC Scopus subject areas

- Analysis