One sided invertibility of matrices over commutative rings, corona problems, and Toeplitz operators with matrix symbols

M. C. Câmara, L. Rodman, Ilya Spitkovsky

    Research output: Contribution to journalArticle

    Abstract

    Conditions are established under which Fredholmness, Coburn's property and one- or two-sided invertibility are shared by a Toeplitz operator with matrix symbol G and the Toeplitz operator with scalar symbol det G. These results are based on one-sided invertibility criteria for rectangular matrices over appropriate commutative rings and related scalar corona type problems.

    Original languageEnglish (US)
    Pages (from-to)58-82
    Number of pages25
    JournalLinear Algebra and Its Applications
    Volume459
    DOIs
    StatePublished - Oct 15 2014

    Fingerprint

    Corona
    Toeplitz Operator
    Invertibility
    Commutative Ring
    Fredholmness
    Scalar

    Keywords

    • Coburn's property
    • Corona problem
    • One-sided invertibility
    • Toeplitz operator
    • Wiener-Hopf factorization

    ASJC Scopus subject areas

    • Algebra and Number Theory
    • Numerical Analysis
    • Geometry and Topology
    • Discrete Mathematics and Combinatorics

    Cite this

    One sided invertibility of matrices over commutative rings, corona problems, and Toeplitz operators with matrix symbols. / Câmara, M. C.; Rodman, L.; Spitkovsky, Ilya.

    In: Linear Algebra and Its Applications, Vol. 459, 15.10.2014, p. 58-82.

    Research output: Contribution to journalArticle

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