### Abstract

It is proved that for certain algebras of continuous functions on compact abelian groups, the set of factorable matrix functions with entries in the algebra is not dense in the group of invertible matrix functions with entries in the algebra, assuming that the dual abelian group contains a subgroup isomorphic to Z3. These algebras include the algebra of all continuous functions and the Wiener algebra. More precisely, it is shown that infinitely many connected components of the group of invertible matrix functions do not contain any factorable matrix functions, again under the same assumption. Moreover, these components actually are disjoint with the subgroup generated by the triangularizable matrix functions.

Original language | English (US) |
---|---|

Pages (from-to) | 1969-1991 |

Number of pages | 23 |

Journal | Journal of Functional Analysis |

Volume | 261 |

Issue number | 7 |

DOIs | |

State | Published - Oct 1 2011 |

### Fingerprint

### Keywords

- Compact abelian groups
- Factorization of Wiener-Hopf type
- Function algebras

### ASJC Scopus subject areas

- Analysis

### Cite this

*Journal of Functional Analysis*,

*261*(7), 1969-1991. https://doi.org/10.1016/j.jfa.2011.05.024

**Non-denseness of factorable matrix functions.** / Brudnyi, Alex; Rodman, Leiba; Spitkovsky, Ilya.

Research output: Contribution to journal › Article

*Journal of Functional Analysis*, vol. 261, no. 7, pp. 1969-1991. https://doi.org/10.1016/j.jfa.2011.05.024

}

TY - JOUR

T1 - Non-denseness of factorable matrix functions

AU - Brudnyi, Alex

AU - Rodman, Leiba

AU - Spitkovsky, Ilya

PY - 2011/10/1

Y1 - 2011/10/1

N2 - It is proved that for certain algebras of continuous functions on compact abelian groups, the set of factorable matrix functions with entries in the algebra is not dense in the group of invertible matrix functions with entries in the algebra, assuming that the dual abelian group contains a subgroup isomorphic to Z3. These algebras include the algebra of all continuous functions and the Wiener algebra. More precisely, it is shown that infinitely many connected components of the group of invertible matrix functions do not contain any factorable matrix functions, again under the same assumption. Moreover, these components actually are disjoint with the subgroup generated by the triangularizable matrix functions.

AB - It is proved that for certain algebras of continuous functions on compact abelian groups, the set of factorable matrix functions with entries in the algebra is not dense in the group of invertible matrix functions with entries in the algebra, assuming that the dual abelian group contains a subgroup isomorphic to Z3. These algebras include the algebra of all continuous functions and the Wiener algebra. More precisely, it is shown that infinitely many connected components of the group of invertible matrix functions do not contain any factorable matrix functions, again under the same assumption. Moreover, these components actually are disjoint with the subgroup generated by the triangularizable matrix functions.

KW - Compact abelian groups

KW - Factorization of Wiener-Hopf type

KW - Function algebras

UR - http://www.scopus.com/inward/record.url?scp=79960318562&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79960318562&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2011.05.024

DO - 10.1016/j.jfa.2011.05.024

M3 - Article

VL - 261

SP - 1969

EP - 1991

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 7

ER -