Quasinormal operators and reflexive subspaces

摘要

In this note we will show the reflexivity of a weak(*)-closed subspace generated by any proper subset of {(T-*)(n), T-n : n epsilon N}, if T is a quasinormal operator. The main tool is a direct integral of subspaces of operators. Relation between the reflexive closure of a direct integral of subspaces and a direct integral of reflexive closure of subspaces is given.