Published online by Cambridge University Press: 17 April 2009
We introduce the notion of hereditarily indecomposable normed space and we prove that this class of normed spaces may be characterised by means of F+ and strictly singular linear relations. We also show that if X is a complex hereditarily indecomposable normed space then every partially continuous linear relation in X with dense domain can be written as λI + S, where λ ∈ ℂ and S is a strictly singular linear relation.