Geodesic
Commutative symmetric operator algebras in a~Pontrjagin space
Izvestiya. Mathematics , Tome 3 (1969) no. 3, pp. 515-535

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In the articles of M. A. Na\v{i}mark a study has been made of commutative symmetric algebras of bounded operators in the space $\mathsf\Pi_k$. 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 Na\v{i}ark'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. 
@article{IM2_1969_3_3_a3,
     author = {A. I. Loginov},
     title = {Commutative symmetric operator algebras in {a~Pontrjagin} space},
     journal = {Izvestiya. Mathematics },
     pages = {515--535},
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     volume = {3},
     number = {3},
     year = {1969},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1969_3_3_a3/}
}
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A. I. Loginov. Commutative symmetric operator algebras in a~Pontrjagin space. Izvestiya. Mathematics , Tome 3 (1969) no. 3, pp. 515-535. http://geodesic.mathdoc.fr/item/IM2_1969_3_3_a3/