A direct decomposition of the measure algebra of a locally compact abelian group
Varopoulos, Nicolas Th.
Annales de l'Institut Fourier, Tome 16 (1966), p. 121-143 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

Une décomposition directe de M(G) [resp. M c (G); M 0 (G)], algèbre des mesures d’un groupe localement compact G [resp. mesures diffuses ; mesures dont la transformée de Fourier s’annule à l’infini] est obtenue ; l’application principale de cette décomposition est de démontrer que M c ≠M c 2 ¯ et que M c 2 ¯≠M 0 .

@article{AIF_1966__16_1_121_0,
     author = {Varopoulos, Nicolas Th.},
     title = {A direct decomposition of the measure algebra of a locally compact abelian group},
     journal = {Annales de l'Institut Fourier},
     volume = {16},
     year = {1966},
     pages = {121-143},
     doi = {10.5802/aif.228},
     mrnumber = {34 \#3227},
     zbl = {0143.15801},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1966__16_1_121_0}
}

Varopoulos, Nicolas Th. A direct decomposition of the measure algebra of a locally compact abelian group. Annales de l'Institut Fourier, Tome 16 (1966) pp. 121-143. doi : 10.5802/aif.228. http://gdmltest.u-ga.fr/item/AIF_1966__16_1_121_0/

[1] N. Bourbaki, Livre VI Intégration.

[2] N. Bourbaki, Utilisation des nombres réels en topologie générale, Livre III Topologie générale, ch. 9. | Zbl 0031.05502

[3] E. Hewitt, Michigan Math. J., 5 (1958), 149-158. | Zbl 0085.10003

[4] W. Rudin, Fourier analysis on groups, Interscience Tract No. 12. | MR 27 #2808 | Zbl 0107.09603

[5] L. Schwartz, Produits Tensoriels Topologiques, etc., Séminaire (1953-1954), Faculté des Sciences de Paris. | Zbl 0059.10401

[6] A. B. Simon, Homomorphisms on measure algebras, Illinois J. of Math., 5 (1961), 398-408. | MR 24 #A1635 | Zbl 0114.31204

[7] A. B. Simon, The ideal space and Silov boundary of a subalgebra of measures on a group, J. Math. Anal. and Appl., 6 (1963), 266-276. | MR 26 #6804 | Zbl 0124.07001

[8] N. Th. Varopoulos, Sets of Multiplicity in locally compact abelian groups. (to appear). | Zbl 0145.03501

[9] N. Th. Varopoulos, A theorem on the continuity of homomorphisms of locally compact groups, Proc. Camb. Phil. Soc. (1964), 60, 449. | MR 29 #184 | Zbl 0121.03704