Field algebras in quantum theory with indefinite metric. II. Formulation of a modular theory in Pontryagin space

The formalism of modular theory for $J$-symmetric weakly closed algebras in Pontryagin space is introduced. Some propositions about the properties of the generalized $J$-Hilbert algebras $\mathscr U$ and $\mathscr U'$ are proved. The main tool in the proofs is the definitizing operator method.