Elementary operators on strongly double triangle subspace lattice algebras

Let Di be a strongly double triangle subspace lattice on a Banach space Xi, where i=1,2. If operator pair (M,M∗) is a surjective elementary operator on , then there exist closed, densely defined linear operators from the domain of in X1 into X2 and from the domain of in X2 into X1 satisfying and for all such that and .