Semi-amenability and Connes Semi-amenability of Banach Algebras

Let A be a Banach algebra and X a Banach Abimodule, the derivation D : A → X is semiinner if there are ξ, μ ∈ X such that D(a) = a.ξ − μ.a, (a ∈ A). A is called semiamenable if every derivation D : A → X∗ is semiinner. The dual Banach algebra A is Connes semiamenable (resp. approximately semiamenable) if, every D ∈ Z^1_w * (A,X), for each normal, dual Banach Abimodule X, is semi inner (resp. approximately semiinner). We will investigate on some properties of semiamenability and Connes semiamenability of Banach algebras which former have been studied for amenability case.