On Closed Ideals in a Certain Class of Algebras of Holomorphic Functions

Canadian mathematical bulletin

Antoni Wawrzynczyk¹  Héctor Merino-Cruz² 

[1] Departamento de Matemáticas, Universidad Autónoma Metropolitana-Izta-palapa AP 55-534, 09340 México D. F., México;Universidad Autónoma de Guerrero , Unidad Académica de Matemáticas , Av. Lázaro Cárdenas S/N, Col. La Haciendita , 39127 Chilpancingo, Gro., México

关键词: Banach algebra;    disc algebra;    holomorphic spaces;    standard ideal;   

DOI  :  10.4153/CMB-2015-003-6

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We recently introduced a weighted Banach algebra $mathfrak{A}_G^n$ of functions which are holomorphic on the unit disc $mathbb{D}$, continuous up to the boundary and of the class $C^{(n)}$ at all points where the function $G$ does not vanish. Here, $G$ refers to a function of the disc algebra without zeros on $mathbb{D}$. Then we proved that all closed ideals in $mathfrak{A}_G^n$ with at most countable hull are standard. In the present paper, on the assumption that $G$ is an outer function in $C^{(n)}(overline{mathbb{D}})$ having infinite roots in $mathfrak{A}_G^n$ and countable zero set $h(G)$, we show that all theclosed ideals $I$ with hull containing $h(G)$ are standard.

【 授权许可】

Unknown