Idempotent maximal ideals and independent sets
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- by Colin C. Graham PDF
- Proc. Amer. Math. Soc. 54 (1976), 133-137 Request permission
Abstract:
Let $E$ be a compact independent subset of a nondiscrete LCA group $G$. Let $GpE$ be the subgroup of $G$ generated algebraically by $E$. If $\mu$ is a continuous, regular, Borel measure on $GpE$ with $\mu (GpE) \ne 0$, then there exists a maximal ideal $\chi$ of the algebra $M(G)$ of regular Borel measures on $G$ such that the restriction of $\chi$ to ${L^1}(\mu ) = \{ \nu \in M(G):\nu \ll \mu \}$ is a nontrivial idempotent in ${L^\infty }(\mu )$. This result is used to give a new proof that $GpE$ has zero Haar measure.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 133-137
- DOI: https://doi.org/10.1090/S0002-9939-1976-0390645-6
- MathSciNet review: 0390645