Finitely-generated left ideals in Banach algebras on groups and semigroups
Finitely-generated left ideals in Banach algebras on groups and semigroups
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群和半群上巴拿赫代数的有限生成左理想
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发表时间：
2016
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通讯作者：
Jared T. White
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作者：
Jared T. White
设G是局部紧群.证明了L1（G）中的增广理想是（代数上）有限生成的左理想当且仅当G是有限的。然后，我们调查这个结果的加权版本，以及一个版本的半群代数。加权测度代数也被认为是。我们的动机是最近的猜想戴尔斯和oedelazko，其中指出，一个单位的Banach代数，其中每个极大左理想是有限生成的必然是有限维的。我们证明，这一猜想持有的许多代数考虑。最后，我们使用的理论，我们已经开发出的交换Banach代数，涉及到格里森定理的一些例子。
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.