# Journal of Operator Theory

Volume 37, Issue 2, Spring 1997 pp. 201-222.

A description of commutative symmetric operator algebras in a Pontryagin space $\Pi_1$**Authors**: Oleg Ya. Bendersky (1), Semyon N. Litvinov (2) and Vladimir I. Chilin (3)

**Author institution:**(1) Department of Mathematics, Tashkent State University, Vuzgorodok, 700095 Tashkent, UZBEKISTAN, CIS. Current address: Misholdardar 6/4, Eilat - 88000, ISRAEL

(2) Department of Mathematics, Tashkent State University, Vuzgorodok, 700095 Tashkent, UZBEKISTAN, CIS. Current address: Mathematics Department, Minard 300, North Dakota State University, Fargo, ND 58105, USA

(3) Department of Mathematics, Tashkent State University, Vuzgorodok, 700095 Tashkent, UZBEKISTAN, CIS

**Summary:**We construct a system of model commutative symmetric operator algebras (c.s.o.a.) in a Pontryagin space $\Pi_1$ such that both the weak operator and the uniform operator closures of any c.s.o.a. in $\Pi_1$ can be described in terms of the models found. We then use that representation to obtain the theorem of bicommutant for a c.s.o.a. in $\Pi_1$.

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