Analog of Posner's theorem for (a, β) -derivation

Analog of Posner's theorem for (a, β) -derivation

Let A ba a Banach algebra and a, β be automorphisms on A. A linear map d on A is called (a; β)-derivation if d(ab) = a(a)d(b) + d(a)B(b), (a; b ∈ A). In this article we extend Posnerʹs theorem for (a, b)-derivations d1 and d2. We characterize when the product d1d2 is a (a, β)-derivation.