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October 2019 Extensions of uniform algebras
Sam Morley
Banach J. Math. Anal. 13(4): 837-863 (October 2019). DOI: 10.1215/17358787-2018-0040

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 realized 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.

Citation

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Sam Morley. "Extensions of uniform algebras." Banach J. Math. Anal. 13 (4) 837 - 863, October 2019. https://doi.org/10.1215/17358787-2018-0040

Information

Received: 30 August 2018; Accepted: 14 November 2018; Published: October 2019
First available in Project Euclid: 9 October 2019

zbMATH: 07118765
MathSciNet: MR4016900
Digital Object Identifier: 10.1215/17358787-2018-0040

Subjects:
Primary: 46J10
Secondary: 47B48

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.13 • No. 4 • October 2019
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