Asymmetric maximal ideals in

Author:
Sadahiro Saeki

Journal:
Trans. Amer. Math. Soc. **222** (1976), 241-254

MSC:
Primary 43A10

DOI:
https://doi.org/10.1090/S0002-9947-1976-0415201-7

MathSciNet review:
0415201

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Abstract: Let *G* be a nondiscrete LCA group, the measure algebra of *G*, and the closed ideal of those measures in whose Fourier transforms vanish at infinity. Let and be the spectrum of , the set of all symmetric elements of , and the spectrum of , respectively. In this paper this is shown: Let be a separable subset of . Then there exist a probability measure in and a compact subset *X* of such that for each and each

*G*is -compact and is empty otherwise, and (d) for each the set contains the topological boundary of in the complex plane.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1976-0415201-7

Keywords:
LCA group,
measure algebra,
asymmetric maximal ideal,
-boundary

Article copyright:
© Copyright 1976
American Mathematical Society