Document Type : Original Paper

Author

• B. Mohammadzadeh

Department of Mathematics, Faculty of Sciences, Babol University of Technology, Babol, Mazandaran, Islamic Republic of Iran

Abstract

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 .

Keywords

• Complemented subspace
• Foundation semigroup
• Semigroup algebras