Extensions of Uniform Algebras

Morley, Sam (2019) Extensions of Uniform Algebras. Banach Journal of Mathematical Analysis, 13 (4). pp. 837-863. ISSN 1735-8787

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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.

Item Type: Article
Uncontrolled Keywords: uniform algebras,uniform algebra extensions,averaging operators,cole extensions,analysis ,/dk/atira/pure/subjectarea/asjc/2600/2603
Faculty \ School: Faculty of Science > School of Mathematics
Related URLs:
Depositing User: LivePure Connector
Date Deposited: 20 Sep 2019 09:30
Last Modified: 11 Nov 2020 01:08
URI: https://ueaeprints.uea.ac.uk/id/eprint/72311
DOI: 10.1215/17358787-2018-0040

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