Geodesic
Nondegenerate operator algebras in spaces with an indefinite metric
Izvestiya. Mathematics , Tome 7 (1973) no. 3, pp. 529-534.

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A theorem on the bicommutant is proved for nondegenerate $\mathcal J$-symmetric operator algebras in the space $\Pi_k$ ($k\infty$). By means of this theorem a simple description is given of the set of unitarily equivalent classes of nondegenerate, weakly closed $\mathcal J$-symmetric algebras. 
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V. I. Liberzon; V. S. Shul'man. Nondegenerate operator algebras in spaces with an indefinite metric. Izvestiya. Mathematics , Tome 7 (1973) no. 3, pp. 529-534. http://geodesic.mathdoc.fr/item/IM2_1973_7_3_a3/

[1] Ismagilov R. S., “Algebry operatorov v prostranstvakh s indefinitnoi metrikoi”, Dokl. AN SSSR, 158:2 (1964), 268–270 | MR | Zbl

[2] Naimark M. A., Normirovannye koltsa, Nauka, M., 1968 | MR | Zbl

[3] Iokhvidov I. S., Krein M. G., “Spektralnaya teoriya operatorov v prostranstve s indefinitnoi metrikoi”, Tr. Mosk. Matem. ob-va, 5, 1956, 367–432