Hyperinvariant, characteristic and marked subspaces

Abstract

Let V be a finite dimensional vector space over a field K and f a K-endomorphism of V. In this paper we study three types of f -invariant subspaces, namely hyperinvariant sub- spaces, which are invariant under all endomorphisms of V that commute with f , characteristic subspaces, which remain fixed under all automorphisms of V that commute with f ,a nd marked subspaces, which have a Jordan basis (with respect to f|X ) that can be extended to a Jordan basis of V. We show that a subspace is hyperinvariant if and only if it is characteristic and marked. If K has more than two elements then each characteristic subspace is hyperinvariant.