On the contracted l1-algebra of a 0-bisimple inverse semigroup

Abstract

Let S be a 0-bisimple inverse semigroup and let denote the contracted l1-algebra of S; that is, the Banach algebra l1 (S)/Z, where Z is the ideal spanned by the zero of S. It is shown that, if l1 (G) is primitive for some non-zero maximal subgroup G of S, then is primitive. The same result also holds with primitivity replaced by a stronger condition, here called *-primitivity