TY - JOUR ID - 50488 TI - Weak*-closed invariant subspaces and ideals of semigroup algebras on foundation semigroups JO - Journal of Sciences, Islamic Republic of Iran JA - JSCIENCES LA - en SN - 1016-1104 AU - Mohammadzadeh, B. AD - Department of Mathematics, Faculty of Sciences, Babol University of Technology, Babol, Mazandaran, Islamic Republic of Iran Y1 - 2014 PY - 2014 VL - 25 IS - 1 SP - 51 EP - 55 KW - Complemented subspace KW - Foundation semigroup KW - Semigroup algebras DO - N2 - 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 . UR - https://jsciences.ut.ac.ir/article_50488.html L1 - https://jsciences.ut.ac.ir/article_50488_8bcf6c5a22fd9a2f7939bec5ecac6979.pdf ER -