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Measures vanishing off the symmetric maximal ideals of M(G)†

Published online by Cambridge University Press:  24 October 2008

Colin C. Graham
Colin C. Graham
Affiliation:
Northwestern University, Illinois 60201
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Abstract

We show that if μ is a measure on the LCA group G whose Gelfand transform vanishes off the set Σ of symmetric maximal ideals, then μ µ M0(G), that is, then the Fourier-Steiltjes transform of μ vanishes at infinity. This result is then used to show μ µ L1(G)½.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 75 , Issue 1 , January 1974 , pp. 51 - 61
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

(1)Brown, G.M 0(G) has a symmetric maximal ideal off the Shilov boundary. Proc. London Math. Soc. (3) 27 (1973), 484–504.CrossRefGoogle Scholar
(2)Brown, G. and Moran, W.L-ideals of M(G) determined by continuity of translation, Proc. Edinburgh Math. Soc., to appear.Google Scholar
(3)Brown, G. and Moran, W.L ½(G) is the kernel of the asymmetric maximal ideals of M(G). Bull. London Math. Soc. 5 (1973), 179–186.CrossRefGoogle Scholar
(4)Drury, S. W.Properties of certain measures on a topological group. Proc. Cambridge Philos. Soc. 64 (1968), 1011–1013.CrossRefGoogle Scholar
(5)Graham, C. C.Compact independent sets and Haar measure. Proc. Amer. Math. Soc. 36 (1972), 578–582.Google Scholar
(6)Graham, C. C.M 0(G) is not a prime L-ideal of measures. Proc. Amer. Math. Soc. 27 (1971), 557–562.Google Scholar
(7)Halmos, P.Measure theory, Van Nostrand, Princeton N.J., 1950.CrossRefGoogle Scholar
(8)Knufman, R.A functional method for linear sets, Israel J. Math. 5 (1967), 185–187.CrossRefGoogle Scholar
(9)Rago, J. Thesis, Northwestern Univ., 1972.Google Scholar
(10)Rickart, C.General Theory of Banach Algebras. Van Nostrand, Princeton, N.J., 1960.Google Scholar
(11)Rudin, W.Fourier Analysis on Groups, Wiley, New York, 1962 MR27, no. 2808.Google Scholar
(12)Shimizu, T.L-ideals of measure algebras, Proc. Japan Acad. 48 (1972), 172–176.Google Scholar
(13)Taylor, J. L.The structure of convolution measure algebras. Trans. Amer. Math. Soc. 119 (1965), 150–166.CrossRefGoogle Scholar
(14)Taylor, J. L.Measure Algebras, CBMS Conference Report no. 16, Amer. Math. Soc., Providence, R.I., 1973.CrossRefGoogle Scholar