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 |
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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 journal › Article
}
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
VL - 459
SP - 58
EP - 82
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
SN - 0024-3795
ER -