Geodesic
Operator algebras and invariant subspaces lattices.~II
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 19, Tome 190 (1991), pp. 110-147

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Given a bounded linear operator $T$, we study the following questions: when the сommutant $\{T\}'$ is commutative; when each operator in the bicommutant $\{T\}''$ can be approximated by polynomials of $T$ in the weak operator topology, the problem of reflexivity, and others. These questions are solved for some classes of operators. 
@article{ZNSL_1991_190_a5,
     author = {V. V. Kapustin and A. V. Lipin},
     title = {Operator algebras and invariant subspaces {lattices.~II}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {110--147},
     publisher = {mathdoc},
     volume = {190},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1991_190_a5/}
}
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V. V. Kapustin; A. V. Lipin. Operator algebras and invariant subspaces lattices.~II. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 19, Tome 190 (1991), pp. 110-147. http://geodesic.mathdoc.fr/item/ZNSL_1991_190_a5/