On the range of a homomorphism of a group algebra into a measure algebra

Author:
Jyunji Inoue

Journal:
Proc. Amer. Math. Soc. **43** (1974), 94-98

MSC:
Primary 43A22

MathSciNet review:
0330926

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Abstract: It is shown, that if is a LCA group and if is a nondiscrete LCA group then there exists a proper closed subalgebra of the measure algebra of (independent of the choice of ) in which the range of every homomorphism of the group algebra of into the measure algebra of is contained.

**[1]**Paul J. Cohen,*On a conjecture of Littlewood and idempotent measures*, Amer. J. Math.**82**(1960), 191–212. MR**0133397****[2]**Paul J. Cohen,*On homomorphisms of group algebras*, Amer. J. Math.**82**(1960), 213–226. MR**0133398****[3]**P. Eymard,*Homomorphismes des algèbres de groupe*, Séminaire Bourbaki, 1961/62, n 231.**[4]**Jyunji Inoue,*Some closed subalgebras of measure algebras and a generalization of P. J. Cohen’s theorem*, J. Math. Soc. Japan**23**(1971), 278–294. MR**0290038****[5]**Takasi Itô and Ichiro Amemiya,*A simple proof of the theorem of P. J. Cohen*, Bull. Amer. Math. Soc.**70**(1964), 774–776. MR**0167590**, 10.1090/S0002-9904-1964-11233-7**[6]**Walter Rudin,*Fourier analysis on groups*, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley and Sons), New York-London, 1962. MR**0152834**

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DOI:
https://doi.org/10.1090/S0002-9939-1974-0330926-3

Keywords:
Homomorphisms of group algebras,
measure algebras,
LCA groups,
range of homomorphisms

Article copyright:
© Copyright 1974
American Mathematical Society