Sur un problème de I. Glicksberg : les idéaux fermés de type fini de M(G)
Annales de l'Institut Fourier, Volume 28 (1978) no. 3, p. 143-164
G is a locally compact abelian group, M(G) the convolution algebras of bounded Radon measures on G. The following statements are equivalent: a) μ*M(G) is closed b) μ*L 1 (G) is closed c) μ=η*ν, where η is idempotent and ν invertible.
Soit μM(G), algèbre de convolution des mesures de Radon bornées sur le groupe abélien localement compact G. Pour que μ*M(G) soit fermé dans M(G) (ou, ce qui revient au même, pour que μ*L 1 (G) soit fermé), il faut et il suffit que μ soit la convolution d’une mesure inversible et d’une mesure idempotente.
@article{AIF_1978__28_3_143_0,
     author = {Host, Bernard and Parreau, Fran\c cois},
     title = {Sur un probl\`eme de I. Glicksberg : les id\'eaux ferm\'es de type fini de $M(G)$},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {28},
     number = {3},
     year = {1978},
     pages = {143-164},
     doi = {10.5802/aif.706},
     mrnumber = {80b:43003},
     zbl = {0368.43001},
     language = {fr},
     url = {https://aif.centre-mersenne.org/item/AIF_1978__28_3_143_0}
}
Host, Bernard; Parreau, François. Sur un problème de I. Glicksberg : les idéaux fermés de type fini de $M(G)$. Annales de l'Institut Fourier, Volume 28 (1978) no. 3, pp. 143-164. doi : 10.5802/aif.706. https://aif.centre-mersenne.org/item/AIF_1978__28_3_143_0/

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