Projective free algebras of continuous functions on compact abelian groups

Alex Brudnyi, Leiba Rodman, Ilya M. Spitkovsky

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)918-932
Number of pages15
JournalJournal of Functional Analysis
Volume259
Issue number4
DOIs
StatePublished - Aug 2010

Keywords

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

ASJC Scopus subject areas

  • Analysis

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