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

被引:7
|
作者
White, Jared T. [1 ]
机构
[1] Univ Lancaster, Dept Math & Stat, Lancaster LA1 4YF, England
关键词
maximal left ideal; Banach algebra; finitely-generated; augmentation ideal; group algebra; weighted group algebra; semigroup algebra; Gleason's theorem; MAXIMAL LEFT IDEALS;
D O I
10.4064/sm8743-1-2017
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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 Zelazko, 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.
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页码:67 / 99
页数:33
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