Closed ideals in a new class of algebras of holomorphic functions on the disc

Hector Merino-Cruz, and Antoni Wawrzyńczyk. "Closed ideals in a new class of algebras of holomorphic functions on the disc." Commentationes Mathematicae 54.1 (2014): null. <http://eudml.org/doc/292472>.

@article{HectorMerino2014,
abstract = {We define a new class of Banach algebras of holomorphic functions on the unit disc $\mathbb \{D\}$ which contains the algebras studied in [GMR2] and [GW]. To a function G of the class $\mathcal \{A\}^1 (\mathbb \{D\})$ nowhere vanishing in $\mathbb \{D\}$ we associate a Banach algebra $\mathcal \{A\}^n_G (\mathbb \{D\})$ contained in the disc algebra $\mathcal \{A\}(\mathbb \{D\})$. We prove that all closed ideals of $\mathcal \{A\}^n_G (\mathbb \{D\})$ of at most countable hull are of the standard form.},
author = {Hector Merino-Cruz, Antoni Wawrzyńczyk},
journal = {Commentationes Mathematicae},
keywords = {Banach algebra, disc algebra, standard ideal},
language = {eng},
number = {1},
pages = {null},
title = {Closed ideals in a new class of algebras of holomorphic functions on the disc},
url = {http://eudml.org/doc/292472},
volume = {54},
year = {2014},
}

TY - JOUR
AU - Hector Merino-Cruz
AU - Antoni Wawrzyńczyk
TI - Closed ideals in a new class of algebras of holomorphic functions on the disc
JO - Commentationes Mathematicae
PY - 2014
VL - 54
IS - 1
SP - null
AB - We define a new class of Banach algebras of holomorphic functions on the unit disc $\mathbb {D}$ which contains the algebras studied in [GMR2] and [GW]. To a function G of the class $\mathcal {A}^1 (\mathbb {D})$ nowhere vanishing in $\mathbb {D}$ we associate a Banach algebra $\mathcal {A}^n_G (\mathbb {D})$ contained in the disc algebra $\mathcal {A}(\mathbb {D})$. We prove that all closed ideals of $\mathcal {A}^n_G (\mathbb {D})$ of at most countable hull are of the standard form.
LA - eng
KW - Banach algebra, disc algebra, standard ideal
UR - http://eudml.org/doc/292472
ER -