Non-denseness of factorable matrix functions

Alex Brudnyi, Leiba Rodman, Ilya M. Spitkovsky

Research output: Contribution to journalArticle

Abstract

It is proved that for certain algebras of continuous functions on compact abelian groups, the set of factorable matrix functions with entries in the algebra is not dense in the group of invertible matrix functions with entries in the algebra, assuming that the dual abelian group contains a subgroup isomorphic to Z3. These algebras include the algebra of all continuous functions and the Wiener algebra. More precisely, it is shown that infinitely many connected components of the group of invertible matrix functions do not contain any factorable matrix functions, again under the same assumption. Moreover, these components actually are disjoint with the subgroup generated by the triangularizable matrix functions.

Original languageEnglish (US)
Pages (from-to)1969-1991
Number of pages23
JournalJournal of Functional Analysis
Volume261
Issue number7
DOIs
StatePublished - Oct 1 2011

Keywords

  • Compact abelian groups
  • Factorization of Wiener-Hopf type
  • Function algebras

ASJC Scopus subject areas

  • Analysis

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