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Weak-star continuous homomorphisms and a decomposition of orthogonal measures

B. J. Cole, Theodore W. Gamelin (1985)

Annales de l'institut Fourier

We consider the set S ( μ ) of complex-valued homomorphisms of a uniform algebra A which are weak-star continuous with respect to a fixed measure μ . The μ -parts of S ( μ ) are defined, and a decomposition theorem for measures in A ⊥ ∩ L 1 ( μ ) is obtained, in which constituent summands are mutually absolutely continuous with respect to representing measures. The set S ( μ ) is studied for T -invariant algebras on compact subsets of the complex plane and also for the infinite polydisc algebra.

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