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- W2952565186 abstract "Let $G$ be a locally compact group. We prove that the augmentation ideal in $L^1(G)$ is (algebraically) finitely-generated as a left ideal if and only if $G$ is finite. We then investigate weighted versions of this result, as well as a version for semigroup algebras. Weighted measure algebras are also considered. We are motivated by a recent conjecture of Dales and Żelazko, which states that a unital Banach algebra in which every maximal left ideal is finitely-generated is necessarily finite-dimensional. We prove that this conjecture holds for many of the algebras considered. Finally, we use the theory that we have developed to construct some examples of commutative Banach algebras that relate to a theorem of Gleason." @default.
- W2952565186 created "2019-06-27" @default.
- W2952565186 creator A5012482896 @default.
- W2952565186 date "2016-12-18" @default.
- W2952565186 modified "2023-09-27" @default.
- W2952565186 title "Finitely-Generated Left Ideals in Banach Algebras on Groups and Semigroups" @default.
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- W2952565186 hasPublicationYear "2016" @default.
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