Volume 37 • Number 1 • 2014   • On the Radical Banach Algebras Related to Semigroup Algebras Ali Ghaffari Abstract. 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. 2010 Mathematics Subject Classification: Primary: 43A05; Secondary: 46H10 Full text: PDF