Our first purpose in this paper is to provide necessary conditions for a weak＊-closed translation invariant subspace in the semigroup algebra of a locally compact topological foundation semigroup to be completely com...Our first purpose in this paper is to provide necessary conditions for a weak＊-closed translation invariant subspace in the semigroup algebra of a locally compact topological foundation semigroup to be completely complemented. We give conditions when a weak＊-closed left translation invariant subspace in Ma,（S）＊ of a compact cancellative foundation semigroup S is the range of a weak＊-weak＊ continuous projection on M~,（S）＊ commuting with translations. Let G be a locally compact group and A be a Banach G-module. Our second purpose in this paper is to study some projections on A＊ and /3（A＊） which commutes with translations and convolution.展开更多
文摘Our first purpose in this paper is to provide necessary conditions for a weak＊-closed translation invariant subspace in the semigroup algebra of a locally compact topological foundation semigroup to be completely complemented. We give conditions when a weak＊-closed left translation invariant subspace in Ma,（S）＊ of a compact cancellative foundation semigroup S is the range of a weak＊-weak＊ continuous projection on M~,（S）＊ commuting with translations. Let G be a locally compact group and A be a Banach G-module. Our second purpose in this paper is to study some projections on A＊ and /3（A＊） which commutes with translations and convolution.
