%0 Journal Article %T Weak*-closed invariant subspaces and ideals of semigroup algebras on foundation semigroups %J Journal of Sciences, Islamic Republic of Iran %I University of Tehran %Z 1016-1104 %A Mohammadzadeh, B. %D 2014 %\ 03/01/2014 %V 25 %N 1 %P 51-55 %! Weak*-closed invariant subspaces and ideals of semigroup algebras on foundation semigroups %K Complemented subspace %K Foundation semigroup %K Semigroup algebras %R %X 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 . %U https://jsciences.ut.ac.ir/article_50488_8bcf6c5a22fd9a2f7939bec5ecac6979.pdf