Structure of local $W^*$-albebras in relativistic quantum theory

Within the framework of the Haag–Araki algebraic approach to the axiomatic quantm theory of fields, we make a detailed analysis of conditions under which the local $W^*$-algebras of the theory are factors and satisfy the duality theorem. Proofs of both properties, based on the axioms of the Haag–Araki theory, are given.