Weak-star continuous homomorphisms and a decomposition of orthogonal measures

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

Annales de l'Institut Fourier, Tome 35 (1985), p. 149-189 / Harvested from Numdam

Résumé

Nous considérons l’ensemble $S(\mu )$ 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 $S(\mu )$ et nous obtenons un théorème de décomposition pour les mesures dans $A^{\perp } \cap L^1(\mu )$ tel que les éléments de la somme soient mutuellement absolument continus par rapport aux mesures représentatives. L’ensemble $S(\mu )$ est étudié pour les algèbres $T$-invariantes définies sur les sous-ensembles compacts du plan complexe ou encore pour l’algèbre du polydisque infini.

Abstract

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

Détail

Publié le : 1985-01-01

MR 86m:46051 | Zbl 0546.46042

DOI : https://doi.org/10.5802/aif.1004

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