Geodesic
Operator-irreducible symmetric algebras of operators in the $\mathbf\Pi^1$ Pontryagin space
Izvestiya. Mathematics , Tome 5 (1971) no. 5, pp. 1168-1179

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In this paper we prove that operator-irreducible weakly closed algebras (containing the identity) on $\mathbf\Pi^1$ are reflexive, and construct a canonical model of an arbitrary symmetric operator-irreducible algebra on $\mathbf\Pi^1$ with a bounded norm, which is not (spatially) irreducible. 
@article{IM2_1971_5_5_a10,
     author = {V. I. Liberzon and V. S. Shul'man},
     title = {Operator-irreducible symmetric algebras of operators in the $\mathbf\Pi^1$ {Pontryagin} space},
     journal = {Izvestiya. Mathematics },
     pages = {1168--1179},
     publisher = {mathdoc},
     volume = {5},
     number = {5},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1971_5_5_a10/}
}
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V. I. Liberzon; V. S. Shul'man. Operator-irreducible symmetric algebras of operators in the $\mathbf\Pi^1$ Pontryagin space. Izvestiya. Mathematics , Tome 5 (1971) no. 5, pp. 1168-1179. http://geodesic.mathdoc.fr/item/IM2_1971_5_5_a10/