Let A be an algebra, M be an A-bimodule and let D :A→M be a linear map satisfying D(a)b + aD(b) + D(b)a +bD(a) = 0 whenever a, b ∈ A are such that ab = ba = 0. If A is a C∗-algebra with D continuous or A is a matrix algebra, then there exists a derivation δ :A→Msuch that D is equal to δ plus elementary operators.
