Nondegenerate operator algebras in spaces with an indefinite metric

A theorem on the bicommutant is proved for nondegenerate $\mathcal J$-symmetric operator algebras in the space $\Pi_k$ ($k<\infty$). By means of this theorem a simple description is given of the set of unitarily equivalent classes of nondegenerate, weakly closed $\mathcal J$-symmetric algebras.