Operator algebras and lattices of invariant subspaces. II

For a bounded linear operator T the following questions are considered: the commutativity of the commutant {T}, the possibility of approximation in the weak operator topology of the operators from the bicommutant {T} , reflexivity, the equality of other operator algebras and lattices of subspaces connected with the operator T. Answers to this questions are given for operators from certain classes (C₀-contractions, weak contractions, contractions with finite defect indices, etc.).Translated from Zapiski Nauchnykh Seminarov I eningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 190, pp. 110–147, 1991.