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Extensions of Uniform Algebras

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Extensions of Uniform Algebras. / Morley, Sam.

In: Banach Journal of Mathematical Analysis, Vol. 13, No. 4, 09.10.2019, p. 837-863.

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@article{a53c37530ed0467fbb0a390d81ec6cb4,
title = "Extensions of Uniform Algebras",
abstract = "The theory of algebraic extensions of Banach algebras is well established, and there are many constructions which yield interesting extensions. In particular, Cole's method for extending uniform algebras by adding square roots of functions to a given uniform algebra has been used to solve many problems within uniform algebra theory. However, there are numerous other examples in the theory of uniform algebras that can be realised as extensions of a uniform algebra, and these more general extensions have received little attention in the literature. In this paper, we investigate more general classes of uniform algebra extensions. We introduce a new class of extensions of uniform algebras, and show that several important properties of the original uniform algebra are preserved in these extensions. We also show that several well-known examples from the theory of uniform algebras belong to these more general classes of uniform algebra extensions.",
keywords = "Uniform algebras, uniform algebra extensions, averaging operators, Cole extensions",
author = "Sam Morley",
year = "2019",
month = "10",
day = "9",
doi = "10.1215/17358787-2018-0040",
language = "English",
volume = "13",
pages = "837--863",
journal = "Banach Journal of Mathematical Analysis",
issn = "1735-8787",
publisher = "Duke University Press",
number = "4",

}

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TY - JOUR

T1 - Extensions of Uniform Algebras

AU - Morley, Sam

PY - 2019/10/9

Y1 - 2019/10/9

N2 - The theory of algebraic extensions of Banach algebras is well established, and there are many constructions which yield interesting extensions. In particular, Cole's method for extending uniform algebras by adding square roots of functions to a given uniform algebra has been used to solve many problems within uniform algebra theory. However, there are numerous other examples in the theory of uniform algebras that can be realised as extensions of a uniform algebra, and these more general extensions have received little attention in the literature. In this paper, we investigate more general classes of uniform algebra extensions. We introduce a new class of extensions of uniform algebras, and show that several important properties of the original uniform algebra are preserved in these extensions. We also show that several well-known examples from the theory of uniform algebras belong to these more general classes of uniform algebra extensions.

AB - The theory of algebraic extensions of Banach algebras is well established, and there are many constructions which yield interesting extensions. In particular, Cole's method for extending uniform algebras by adding square roots of functions to a given uniform algebra has been used to solve many problems within uniform algebra theory. However, there are numerous other examples in the theory of uniform algebras that can be realised as extensions of a uniform algebra, and these more general extensions have received little attention in the literature. In this paper, we investigate more general classes of uniform algebra extensions. We introduce a new class of extensions of uniform algebras, and show that several important properties of the original uniform algebra are preserved in these extensions. We also show that several well-known examples from the theory of uniform algebras belong to these more general classes of uniform algebra extensions.

KW - Uniform algebras

KW - uniform algebra extensions

KW - averaging operators

KW - Cole extensions

U2 - 10.1215/17358787-2018-0040

DO - 10.1215/17358787-2018-0040

M3 - Article

VL - 13

SP - 837

EP - 863

JO - Banach Journal of Mathematical Analysis

JF - Banach Journal of Mathematical Analysis

SN - 1735-8787

IS - 4

ER -

ID: 165161708