Structural rigidity of generalised Volterra operators on HP

We show that the non-compact generalised analytic Volterra operators T-g, where g is an element of BMOA, have the following structural rigidity property on the Hardy spaces H-P for 1 <= p < infinity and p not equal 2: if T-g is bounded below on an infinite-dimensional subspace M subset of H-P, then M contains a subspace linearly isomorphic to l(p). This implies in particular that any Volterra operator T-g: H-p -> H-p is l(2)-singular for p not equal 2. (C) 2018 Elsevier Masson SAS. All rights reserved.