Rank One Operator In Some Group C*- Algebras

Let G be a locally compact group,λbe the left regular representation ofG on L² (G ). C_δ^* (G )denotes the C^*-algebra generated by {λ( x ):x∈G}and E = E_G is the rank one operator such that E ( g ) = (∫g ( x )d x).1_G,1_G denotes the constant one function onG .In this paper, we summarize some results about the rank one operator in C_δ^* (G ), C_δ^* (G/H), and C_δ^* (G₁×G₂).