Representations of C*-algebras in spaces with indefinite metric

The problem is considered of orthogonalization of J-symmetric representations of C^*-algebras in the Pontryagin spaces π_x. It is proved that in spaces with finite rank of indefiniteness, every such representation is similar to a *-representation in a Hilbert space. Necessary and sufficient conditions are established for the existence of an invariant dual pair of subspaces for a J-symmetric operator algebra.