Some notions of (σ,τ)−amenability for unitization of Banach algebras

Let A be a Banach algebra and σ and τ be continuous endomorphisms on A. In this paper, we investigate (σ,τ)−amenability and (σ,τ)−weak amenability for unitization of Banach algebras, and also the relation between of them. We introduce and study the concepts (σ,τ)−trace extention property, (σ,τ)−I−weak amenability and (σ,τ)−ideal amenability for A and its unitization, where I is a closed two-sided ideal in A.