Non-denseness of factorable matrix functions

Alex Brudnyi, Leiba Rodman, Ilya 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

    Fingerprint

    Matrix Function
    Algebra
    Invertible matrix
    Abelian group
    Continuous Function
    Wiener Algebra
    Subgroup
    Dual Group
    Compact Group
    Connected Components
    Disjoint
    Isomorphic

    Keywords

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

    ASJC Scopus subject areas

    • Analysis

    Cite this

    Non-denseness of factorable matrix functions. / Brudnyi, Alex; Rodman, Leiba; Spitkovsky, Ilya.

    In: Journal of Functional Analysis, Vol. 261, No. 7, 01.10.2011, p. 1969-1991.

    Research output: Contribution to journalArticle

    Brudnyi, A, Rodman, L & Spitkovsky, I 2011, 'Non-denseness of factorable matrix functions', Journal of Functional Analysis, vol. 261, no. 7, pp. 1969-1991. https://doi.org/10.1016/j.jfa.2011.05.024
    Brudnyi, Alex ; Rodman, Leiba ; Spitkovsky, Ilya. / Non-denseness of factorable matrix functions. In: Journal of Functional Analysis. 2011 ; Vol. 261, No. 7. pp. 1969-1991.
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