Hyperinvariant subspaces for trace class perturbations of normal operators and decomposability

Abstract

We prove that a large class of trace-class perturbations of diagonalizable normal operators on a separable, infinite dimensional complex Hilbert space have non-trivial closed hyperinvariant subspaces. Moreover, a large subclass consists of decomposable operators in the sense of Colojoară and Foiaş [3].