Linear relations on hereditarily indecomposable normed spaces

We introduce the notion of hereditaxily indecomposable normed space and we prove that this class of normed spaces may be characterised by means of F+ and strictly singular lineax relations. We also show that if X is a complex hereditaxily indecomposable normed space then every partially continuous linear relation in X with dense domain can be written as lambda I + S, where lambda I + C and S is a strictly singular linear relation.