Operator algebras and lattices of invariant subspaces. I

Abstract

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.).