Geodesic
On the Radical Banach Algebras Related to Semigroup Algebras
Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 1 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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Let $\mathcal{S}$ be a compactly cancellative foundation semigroup with identity. It is well-known that $L_0^\infty(\mathcal{S};M_a(\mathcal{S}))^*$ can be equipped with a multiplication that extends the original multiplication on $M_a(\mathcal{S})$ and makes $L_0^\infty(\mathcal{S};M_a(\mathcal{S}))^*$ a Banach algebra. In this paper, among the other things, it is shown that if $\mathcal{S}$ is a nondiscrete compactly cancellative foundation semigroup with an identity, then the radical of $L_0^\infty(\mathcal{S};M_a(\mathcal{S}))^*$ is infinite-dimensional.
Classification : Primary: 43A05; Secondary: 46H10 
@article{BMMS_2014_37_1_a3,
     author = {Ali Ghaffari},
     title = {On the {Radical} {Banach} {Algebras} {Related} to {Semigroup} {Algebras}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2014},
     volume = {37},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2014_37_1_a3/}
}
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Ali Ghaffari. On the Radical Banach Algebras Related to Semigroup Algebras. Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 1. http://geodesic.mathdoc.fr/item/BMMS_2014_37_1_a3/