Finite-dimensional left ideals in some algebras associated with a locally compact group期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Finite-dimensional left ideals in some algebras associated with a locally compact group

Authors:	M Filali

Institution:	Department of Mathematical Sciences, University of Oulu, SF 90570 Finland

Abstract:	Let be a locally compact group, let $L^{1}(G)$ be its group algebra, let be its usual measure algebra, let $L^{1}(G)^{*}$ be the second dual of $L^{1}(G)$ with an Arens product, and let $LUC(G)^{}$ be the conjugate of the space of bounded, left uniformly continuous, complex-valued functions on with an Arens-type product. We find all the finite-dimensional left ideals of these algebras. We deduce that such ideals exist in $L^{1}(G)$ and if and only if is compact, and in $L^{1}(G)^{}$ (except those generated by right annihilators of $L^{1}(G)^{}$ ) and $LUC(G)^{*}$ if and only if is amenable.

Keywords:	Locally compact group Arens product representation amenable $U$-invariant finite-dimensional left ideal

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