Weak-star continuous homomorphisms and a decomposition of orthogonal measures
Annales de l'Institut Fourier, Volume 35 (1985) no. 1, p. 149-189

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

Nous considérons l’ensemble $S\left(\mu \right)$ des homomorphismes à valeurs complexes d’une algèbre uniforme $A$ qui sont faiblement continus par rapport à une mesure prédéterminée $\mu$. Nous définissons les $\mu$-parties de $S\left(\mu \right)$ et nous obtenons un théorème de décomposition pour les mesures dans ${A}^{\perp }\cap {L}^{1}\left(\mu \right)$ tel que les éléments de la somme soient mutuellement absolument continus par rapport aux mesures représentatives. L’ensemble $S\left(\mu \right)$ est étudié pour les algèbres $T$-invariantes définies sur les sous-ensembles compacts du plan complexe ou encore pour l’algèbre du polydisque infini.

@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},
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, Volume 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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