Extensions of Uniform Algebras

Sam Morley

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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.
Original languageEnglish
Pages (from-to)837-863
Number of pages27
JournalBanach Journal of Mathematical Analysis
Volume13
Issue number4
Early online date13 Sep 2019
DOIs
Publication statusPublished - 9 Oct 2019

Keywords

  • Uniform algebras
  • uniform algebra extensions
  • averaging operators
  • Cole extensions

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