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A functional description of commutative symmetric operator algebras in the Pontryagin space of type II. (Russian) Zbl 0926.47020

The commutative symmetric algebras \(S\) of operators generated by \(J\)-selfadjoint operators in the Pontryagin space \(\Pi_1\) are considered. Complete description of these algebras is given, i.e. it is proved that these symmetric algebras belong to one of five well-known classes [see V. S. Shulman, Mat. Sb., n. Ser. 89(131), 264-279 (1972; Zbl 0252.46082)]. The functional representation of \(S\) is obtained and the functional calculus for \(S\) is constructed.

MSC:

47B50 Linear operators on spaces with an indefinite metric
47A60 Functional calculus for linear operators
46C20 Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.)
47L30 Abstract operator algebras on Hilbert spaces

Citations:

Zbl 0252.46082
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