no. 1
Weak-star continuous homomorphisms and a decomposition of orthogonal measures
Annales de l'Institut Fourier, Tome 35 (1985) no. 1, pp. 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},
     pages = {149--189},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {35},
     number = {1},
     year = {1985},
     doi = {10.5802/aif.1004},
     zbl = {0546.46042},
     mrnumber = {86m:46051},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1004/}
}
TY  - JOUR
AU  - Cole, B. J.
AU  - Gamelin, Theodore W.
TI  - Weak-star continuous homomorphisms and a decomposition of orthogonal measures
JO  - Annales de l'Institut Fourier
PY  - 1985
SP  - 149
EP  - 189
VL  - 35
IS  - 1
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1004/
DO  - 10.5802/aif.1004
LA  - en
ID  - AIF_1985__35_1_149_0
ER  - 
%0 Journal Article
%A Cole, B. J.
%A Gamelin, Theodore W.
%T Weak-star continuous homomorphisms and a decomposition of orthogonal measures
%J Annales de l'Institut Fourier
%D 1985
%P 149-189
%V 35
%N 1
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.1004/
%R 10.5802/aif.1004
%G en
%F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.1004/

[1]W. Arveson, An Invitation to C* Algebras, Springer-Verlag, 1976. | MR | Zbl

[2]K. Barbey and H. König, Abstract analytic function theory and Hardy algebras, Lecture Notes in Math., vol. 593, Springer-Verlag, 1977. | MR | Zbl

[3]A. Browder, Introduction to Function Algebras, Benjamin, 1969. | MR | Zbl

[4]J. Chaumat, Adhérence faible étoile d'algèbres de fractions rationnelles, Ann. Inst. Fourier, Grenoble, 24,4 (1974), 93-120. | Numdam | MR | Zbl

[5]B.J. Cole and T.W. Gamelin, Tight uniform algebras, Journal of Functional Analysis, 46 (1982), 158-220. | MR | Zbl

[6]J.B. Conway, Subnormal operators, Research Notes in Mathematics # 51, Pitman, 1981. | MR | Zbl

[7]J. Dudziak, Spectral mapping theorems for subnormal operators, J. Funct. Anal., 56 (1984), 360-387. | MR | Zbl

[8]T.W. Gamelin, Uniform Algebras, Prentice-Hall, 1969. | MR | Zbl

[9]T.W. Gamelin, Rational Approximation Theory, course lecture notes, UCLA, 1975.

[10]T.W. Gamelin, Uniform algebras on plane sets, in Approximation Theory, Academic Press, 1973, pp. 100-149. | MR | Zbl

[11]T.W. Gamelin and J. Garnett, Bounded approximation by rational functions, Pac. J. Math., 45 (1973), 129-150. | MR | Zbl

[12]I. Glicksberg, Recent results on function algebras, CBMS Regional Conference Series in Mathematics, vol. 11, Am. Math. Society, 1972. | MR | Zbl

[13]I. Glicksberg, Equivalence of certain representing measures, Proc. A.M.S., 82 (1981), 374-376. | MR | Zbl

[14]K. Hoffman and H. Rossi, Extension of positive weak*-continuous functionals, Duke Math. J., 34 (1967), 453-466. | MR | Zbl

[15]H. Konig and G.L. Seever, The abstract F. and M Riesz theorem, Duke Math. J., 36 (1969), 791-797. | MR | Zbl

[16]T. Lyons, Finely holomorphic functions, J. Funct. Anal., 37 (1980), 1-18. | MR | Zbl

[17]D.E. Sarason, Weak-star density of polynomials, J. Reine Angew Math., 252 (1972), 1-15. | MR | Zbl

Cité par Sources :