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 -