Abstract
We construct a complete system of models of complete I-symmetric algebras of operators in a space of type Π1, which leave invariant at least one degenerate subspace in Π1. The results obtained are applied in the proof of an analog of von Neumann's double commutator theorem, and also in the determination of necessary and sufficient conditions for the reflexivity of weakly closed I-symmetric algebras of operators in Π1. Bibliography: 14 items.
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