$L$-ideals of measure algebras
Tetsuhiro Shimizu · Proceedings of the Japan Academy Series A Mathematical Sciences · 1972
1. Introduction.Let G be a non-discrete locally comapct abelian group with the dual group of G.We will denote by M(G) the Banach algebra of all bounded regular Borel measures on G under convolution multiplication.If/, e M(G), then their convolution product will be denoted/..We shall use additive notation or the group operation in G.If/,re M(G), then "(/" will mean " is absolutely continuous with respect to p" and "/+/-" will mean "/ and are mutually singular". Ifis a closed subspace (subalgebra, ideal) of M(G) will be called an L-subspace (L-subalgebra, L-ideal) provided e !):, r e M(G) and