On rings and Banach algebras with skew derivations

In the present paper, we investigate the commutativity of a prime Banach algebra with skew derivations and prove that if A is prime Banach algebra and A has a nonzero continuous linear skew derivation F from A to A such that [F(x(m)); F(eta(n))] - [tau(m); eta(n)] is an element of Z (A) for an integers m = m(x; eta) > 1 and n = n(x; eta) > 1 and sufficiently many x; eta, then A is commutative.