COMMUTATIVE SYMMETRIC OPERATOR ALGEBRAS IN A PONTRJAGIN SPACE
A. I. Loginov · Mathematics of the USSR-Izvestiya · 1969
In the articles of M. A. Naĭmark a study has been made of commutative symmetric algebras of bounded operators in the space Πk. A model was constructed within whose framework all these algebras can be realized, and conditions were found for their unitary equivalence. In the present article a study is made of Naĭmark's model, and some alterations are proposed which lead to a number of important simplifications. We single out the classes of so-called singular and regular algebras; the study of an arbitrary algebra reduces to the study of these. A complete description is given of regular algebras that are closed with respect to the operator norm.