The Functional Representation of Commutative Symmetric Operator Algebras in Pontryagin Space

Abstract

Symmetric operator algebras are the most powerful tools in the investigations in the quantum field theory. Together with well-known C* and W*-algebras acting in the Hilbert space, recently operator algebras acting in the spaces with indefinite metric began to be used in some models of quantized fields. Particularly, these were the operator algebras in Pontryagin space [2]. Unlike deeply developed theory of C* and W*-algebras, the theory of symmetric operator algebras in a π1 space has just begun to develop.