On the bicommutant for one type of J-symmetric nilpotent algebras in Krein spaces

In the present paper we shall consider an operator algebra in a Krein space. One of the interesting questions that arises in this area is a relationship between the algebra and its bicommutant. Here the question will be investigated for a J-symmetric weakly closed algebra that is nilpotent up to the identity operator and has an invariant subspace of a special type