Weak*-closed invariant subspaces and ideals of semigroup algebras on foundation semigroups - B. Mohammadzadeh (Journal of Sciences, Islamic Republic of Iran)
Let S be a locally compact foundation semigroup with identity and                          be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of    In this paper, we prove that  X  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenable if and only if every complemented weak*-closed left translation invariant subspace of   is invariantly  complemented in .