The C*-algebra of singular integral operators with semi-almost periodic coefficients

A. Böttcher, Yu I. Karlovich, Ilya Spitkovsky

    Research output: Contribution to journalArticle

    Abstract

    We establish a Fredholm criterion for the operators belonging to the C*-algebra generated by singular integral operators with semi-almost periodic matrix coefficients. The result is applied to Toeplitz-like operators that are perturbed by integral operators with fixed singularities at infinity, in which case it leads to an effectively verifiable Fredholm criterion together with an index formula. Our approach is based on an isomorphism theorem for C*-algebras associated with C*-dynamical systems and the notion of canonical generalized AP factorization for almost periodic matrix functions.

    Original languageEnglish (US)
    Pages (from-to)445-484
    Number of pages40
    JournalJournal of Functional Analysis
    Volume204
    Issue number2
    DOIs
    StatePublished - Nov 10 2003

    Fingerprint

    Singular Integral Operator
    Periodic Coefficients
    Almost Periodic
    C*-algebra
    C*-dynamical System
    Isomorphism theorems
    Otto Toeplitz
    Matrix Function
    Operator
    Periodic Functions
    Integral Operator
    Factorization
    Infinity
    Singularity
    Coefficient

    Keywords

    • Almost periodic function
    • C*-algebra
    • C*-dynamical system
    • Matrix function
    • Semi-almost periodic function
    • Singular integral operator
    • Toeplitz operator

    ASJC Scopus subject areas

    • Analysis

    Cite this

    The C*-algebra of singular integral operators with semi-almost periodic coefficients. / Böttcher, A.; Karlovich, Yu I.; Spitkovsky, Ilya.

    In: Journal of Functional Analysis, Vol. 204, No. 2, 10.11.2003, p. 445-484.

    Research output: Contribution to journalArticle

    Böttcher, A. ; Karlovich, Yu I. ; Spitkovsky, Ilya. / The C*-algebra of singular integral operators with semi-almost periodic coefficients. In: Journal of Functional Analysis. 2003 ; Vol. 204, No. 2. pp. 445-484.
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