Finitely-generated left ideals in Banach algebras on groups and semigroups

White, Jared (2017) Finitely-generated left ideals in Banach algebras on groups and semigroups. Studia Mathematica, 239. pp. 67-99. ISSN 0039-3223

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Abstract

Let G be a locally compact group. We prove that the augmentation ideal in L1(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.

Item Type:
Journal Article
Journal or Publication Title:
Studia Mathematica
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
87090
Deposited By:
Deposited On:
18 Jul 2017 12:38
Refereed?:
Yes
Published?:
Published
Last Modified:
22 Nov 2020 04:59