  Motivated by the study of the operator forms of the constant classical
Yang-Baxter equation given by Semonov-Tian-Shansky, Kupershmidt and the others,
we try to construct the rational solutions of the classical Yang-Baxter
equation with parameters by certain linear operators. The fact that the
rational solutions of the CYBE for the simple complex Lie algebras can be
interpreted in term of certain linear operators motivates us to give the notion
of $\mathcal O$-operators such that these linear operators are the $\mathcal
O$-operators associated to the adjoint representations. Such a study can be
generalized to the Lie algebras with nondegenerate symmetric invariant bilinear
forms. Furthermore we give a construction of a rational solution of the CYBE
from an $\mathcal O$-operator associated to the coadjoint representation and an
arbitrary representation with a trivial product in the representation space
respectively.
