Geodesic
Operator algebras and invariant subspaces lattices.~I
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 18, Tome 178 (1989), pp. 23-56

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Given a bounded linear operator $T$, we study the following questions: when the commutant $\{T\}'$ is commutative; when each operator in the bicomrautant $\{T\}''$ 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_1989_178_a1,
     author = {V. V. Kapustin and A. V. Lipin},
     title = {Operator algebras and invariant subspaces {lattices.~I}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {23--56},
     publisher = {mathdoc},
     volume = {178},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1989_178_a1/}
}
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V. V. Kapustin; A. V. Lipin. Operator algebras and invariant subspaces lattices.~I. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 18, Tome 178 (1989), pp. 23-56. http://geodesic.mathdoc.fr/item/ZNSL_1989_178_a1/