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

M. C. Câmara, L. Rodman, I. M. 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

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

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