Weak-star continuous homomorphisms and a decomposition of orthogonal measures
Annales de l'Institut Fourier, Tome 35 (1985) no. 1, p. 149-189
Nous considérons l’ensemble S(μ) des homomorphismes à valeurs complexes d’une algèbre uniforme A qui sont faiblement continus par rapport à une mesure prédéterminée μ. Nous définissons les μ-parties de S(μ) et nous obtenons un théorème de décomposition pour les mesures dans A L 1 (μ) tel que les éléments de la somme soient mutuellement absolument continus par rapport aux mesures représentatives. L’ensemble S(μ) est étudié pour les algèbres T-invariantes définies sur les sous-ensembles compacts du plan complexe ou encore pour l’algèbre du polydisque infini.
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.
@article{AIF_1985__35_1_149_0,
     author = {Cole, B. J. and Gamelin, Theodore W.},
     title = {Weak-star continuous homomorphisms and a decomposition of orthogonal measures},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {35},
     number = {1},
     year = {1985},
     pages = {149-189},
     doi = {10.5802/aif.1004},
     zbl = {0546.46042},
     mrnumber = {86m:46051},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1985__35_1_149_0}
}
Cole, B. J.; Gamelin, Theodore W. Weak-star continuous homomorphisms and a decomposition of orthogonal measures. Annales de l'Institut Fourier, Tome 35 (1985) no. 1, pp. 149-189. doi : 10.5802/aif.1004. http://www.numdam.org/item/AIF_1985__35_1_149_0/

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