Abstract
LetG be a discrete abelian group,Ĝ the character group ofG, andl ∞(G)* the conjugate ofl ∞(G) equipped with an Arens product. In many cases, we can find unitary functionsf such that χf is almost convergent to zero for all χ∈Ĝ. Some of these functions are then used to produce elements μ∈l ∞(G)* such that γμ=0 whenever γ is an annihilator ofC 0(G). Regarded as Borel measures on βG, these elements satisfyxμ=0 for allx∈βG/G. They belong to the radical ofl ∞(G)*, and each of them generates a left ideal ofl ∞(G)* that contains no minimal left ideal.
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Communicated by J. S. Pym
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Filali, M. On some special measures on βG . Semigroup Forum 48, 163–168 (1994). https://doi.org/10.1007/BF02573666
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DOI: https://doi.org/10.1007/BF02573666