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

A. Böttcher, Yu I. Karlovich, Ilya M. 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

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

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