Réflexivité d’une extension d’un opérateur normal par un opérateur nilpotent

Let T be an extension of a one to one normal operator A by a nilpotent operator N. In this paper we calculate the defect of reflexivity of T. We give a necessary and sufficient condition to insure the reflexivity of such extensions. In particular, it is shown that T is reflexive when N is reflexive. © 2005 Elsevier Inc. All rights reserved.