A well-known theorem of E. Posner  states that if the composition d1d2 of derivations d1d2 of a prime ring A of characteristic not 2 is a derivation, then either d1 = 0 or d2 = 0. A number of authors have generalized this theorem in several ways (see e.g. , , and , where further references can be found). Under stronger assumptions when A is the algebra of all bounded linear operators on a Banach space (resp. Hilbert space), Posner's theorem was reproved in  (resp. ). Recently, M. Mathieu  extended Posner's theorem to arbitrary C*-algebras.
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