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Gleason parts for measure algebras

Published online by Cambridge University Press:  24 October 2008

Gavin Brown
Affiliation:
University of Liverpool
William Moran
Affiliation:
University of Liverpool

Extract

We shall verify Miller's conjectured characterization of parts in measure algebras and obtain also a simpler proof of the main result of (2). The basic pattern of argument follows Miller while the chief novelty resides in the approximation method using Wiener–Ditkin sets which is introduced in section 2.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

REFERENCES

(1)Gamelin, T.Uniform Algebras, Prentice-Hall, Engelwood Cliffs N.J., 1969.Google Scholar
(2)Miller, R. R.Gleason parts and Choquet boundary points in convolution measure algebras, Pacific J. Math. 31 (1969), 755–71.CrossRefGoogle Scholar
(3)Rudin, W.Fourier analysis on groupa, Interscience, New York, 1962.Google Scholar
(4)Taylor, J. L.The structure of convolution measure algebras. Trans. Amer. Math. Soc. 119 (1965), 150–66.CrossRefGoogle Scholar
(5)Taylor, J. L.Measure Algebras, C.B.M.S. monograph no. 16, Amer. Math. Soc., Providence R.I., 1973.Google Scholar