  The paper is devoted to a development of the theory of self-adjoint operators
in Krein spaces (J-self-adjoint operators) involving some additional properties
arising from the existence of C-symmetries. The main attention is paid to the
recent notion of stable C-symmetry for J-self-adjoint extensions of a symmetric
operator S. The general results are specialized further by studying in detail
the case where S has defect numbers <2,2>.
