Geodesic
Symmetric Banach algebras of operators in a~space of type $\Pi_1$
Sbornik. Mathematics, Tome 18 (1972) no. 2, pp. 267-283

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We construct a complete system of models of complete $I$-symmetric algebras of operators in a space of type $\Pi_1$, which leave invariant at least one degenerate subspace in $\Pi_1$. 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 $\Pi_1$. Bibliography: 14 titles. 
@article{SM_1972_18_2_a7,
     author = {V. S. Shulman},
     title = {Symmetric {Banach} algebras of operators in a~space of type $\Pi_1$},
     journal = {Sbornik. Mathematics},
     pages = {267--283},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1972_18_2_a7/}
}
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V. S. Shulman. Symmetric Banach algebras of operators in a~space of type $\Pi_1$. Sbornik. Mathematics, Tome 18 (1972) no. 2, pp. 267-283. http://geodesic.mathdoc.fr/item/SM_1972_18_2_a7/