Geodesic
On reductive operators and operator algebras
Izvestiya. Mathematics , Tome 10 (1976) no. 4, pp. 799-807

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We prove a theorem on the structure of weakly closed reductive operator algebras. The proof essentially relies on a known result of V. I. Lomonosov on transitive operator algebras containing a nonzero compact operator. We deduce a number of corollaries which apply to the reductivity problem. Bibliography: 20 titles. 
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     author = {A. I. Loginov and V. S. Shulman},
     title = {On reductive operators and operator algebras},
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     year = {1976},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1976_10_4_a7/}
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A. I. Loginov; V. S. Shulman. On reductive operators and operator algebras. Izvestiya. Mathematics , Tome 10 (1976) no. 4, pp. 799-807. http://geodesic.mathdoc.fr/item/IM2_1976_10_4_a7/