Weak-star continuous homomorphisms and a decomposition of orthogonal measures

Cole, B. J.; Gamelin, Theodore W.

doi:10.5802/aif.1004

Cole, B. J. ; Gamelin, Theodore W.

Annales de l'Institut Fourier, Tome 35 (1985) no. 1, pp. 149-189.

Résumé
Abstract

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 $A^{⊥} \cap L^{1} (μ)$ 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 $A^{⊥} \cap L^{1} (μ)$ 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.

MR Zbl

DOI : 10.5802/aif.1004

@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},
     pages = {149--189},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {35},
     number = {1},
     year = {1985},
     doi = {10.5802/aif.1004},
     mrnumber = {86m:46051},
     zbl = {0546.46042},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/aif.1004/}
}

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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. https://www.numdam.org/articles/10.5802/aif.1004/

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