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

Inoue, Jyunji

doi:10.1090/S0002-9939-1974-0330926-3

On the range of a homomorphism of a group algebra into a measure algebra
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by Jyunji Inoue

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

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

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Abstract:

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

References

Paul J. Cohen, On a conjecture of Littlewood and idempotent measures, Amer. J. Math. 82 (1960), 191–212. MR 133397, DOI 10.2307/2372731
Paul J. Cohen, On homomorphisms of group algebras, Amer. J. Math. 82 (1960), 213–226. MR 133398, DOI 10.2307/2372732

Homomorphismes des algèbres de groupe

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 290038, DOI 10.2969/jmsj/02320278
Takasi Itô and Ichiro Amemiya, A simple proof of the theorem of P. J. Cohen, Bull. Amer. Math. Soc. 70 (1964), 774–776. MR 167590, DOI 10.1090/S0002-9904-1964-11233-7
Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0152834