Vol. 31, No. 3, 1969

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Gleason parts and Choquet boundary points in convolution measure algebras

Richard Roy Miller

Vol. 31 (1969), No. 3, 755–771

Let M be a semisimple convolution measure algebra with structure semigroup S. Then each complex homomorphism of M is given by integrating a semicharacter on S. Gleason parts can be defined on Ŝ, the set of semicharacters on S, by considering the function algebra obtained from the transforms of elements of M. We give a partial characterization of the parts of Ŝ utilizing only the functional values of the elements of Ŝ. We then completely characterize the one point parts of Ŝ utilizing only the functional values of elements of Ŝ.

Mathematical Subject Classification
Primary: 46.80
Received: 8 July 1969
Published: 1 December 1969
Richard Roy Miller