Abstract & Overview
Let A be a Banach algebra and let every module-valued derivation from A to any Banach A-bimodule be continuous. We show that if {dm} is a higher derivation from A to a Banach algebra B with continuous d0, then there exist a continuous left A-module homomorphism U : B(A1,B) → B and a sequence {Dm} of module-valued derivations from A intoB(A1,B) such that dm = U ◦Dm (m ≥ 1), and as a consequence {dm} is automatically continuous. We also obtain a partial result concerning innerness of higher derivations on W ∗-algebras.