### 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 language | English (US) |
---|---|

Pages (from-to) | 58-82 |

Number of pages | 25 |

Journal | Linear Algebra and Its Applications |

Volume | 459 |

DOIs | |

State | Published - Oct 15 2014 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Linear Algebra and Its Applications*, vol. 459, pp. 58-82. https://doi.org/10.1016/j.laa.2014.06.038

}

TY - JOUR

T1 - One sided invertibility of matrices over commutative rings, corona problems, and Toeplitz operators with matrix symbols

AU - Câmara, M. C.

AU - Rodman, L.

AU - Spitkovsky, Ilya

PY - 2014/10/15

Y1 - 2014/10/15

N2 - 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.

AB - 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.

KW - Coburn's property

KW - Corona problem

KW - One-sided invertibility

KW - Toeplitz operator

KW - Wiener-Hopf factorization

UR - http://www.scopus.com/inward/record.url?scp=84904300056&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84904300056&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2014.06.038

DO - 10.1016/j.laa.2014.06.038

M3 - Article

AN - SCOPUS:84904300056

VL - 459

SP - 58

EP - 82

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -