  An O-operator is a relative version of a Rota-Baxter operator and, in the Lie
algebra context, is originated from the operator form of the classical
Yang-Baxter equation. We generalize the well-known construction of dendriform
dialgebras and trialgebras from Rota-Baxter algebras to a construction from
O-operators. We then show that this construction from O-operators gives all
dendriform dialgebras and trialgebras. Furthermore there are bijections between
certain equivalence classes of invertible O-operators and certain equivalence
classes of dendriform dialgebras and trialgebras.
