TY - JOUR

T1 - Non-denseness of factorable matrix functions

AU - Brudnyi, Alex

AU - Rodman, Leiba

AU - Spitkovsky, Ilya M.

N1 - Funding Information:
* Corresponding author. E-mail addresses: [email protected] (A. Brudnyi), [email protected] (L. Rodman), [email protected] (I.M. Spitkovsky). 1 Research of this author is supported in part by NSERC. 2 Research of this author supported in part by the Faculty Research Assignment and Plumeri Award at the College of William and Mary.

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

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U2 - 10.1016/j.jfa.2011.05.024

DO - 10.1016/j.jfa.2011.05.024

M3 - Article

AN - SCOPUS:79960318562

SN - 0022-1236

VL - 261

SP - 1969

EP - 1991

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 7

ER -