Factorization in some ideals of Lau algebras with applications to semigroup algebras

Let A be a Lau algebra with a bounded approximate identity, and let I-0(A) denote the kernel of the identity element in the dual W*-algebra of A. Here, we show that I-0(A) = I-0(A)(2). We also give some applications of this result to closed ideals of codimension one in Banach algebras related to locally compact semigroups.