LAUSR

In this paper we prove that if S is a set of operators acting on a separable Lp-space X, 1 ≤ p < ∞ (or, more generally, on any separable Köthe function space) such that S is indecomposable (that is, no non-trivial subspace of X of the form Lp(A), where A is measurable, is a common S-invariant subspace), then $$\overline {span} $$span¯S admits an indecomposable operator. As applications, we obtain some new results about transitive algebas on separable Hilbert spaces, as well as an extension of the simultaneous Wielandt theorem to semigroups of operators acting on separable Lp-spaces.