On normal crossings in a Banach space

We show that if A is a closed complex analytic subset of a Banach space X with an unconditional basis (e.g., X = ℓ 2 ) that has only normal crossings for singularities, then the structure and ideal sheaves of A are cohesive sheaves over X, and consequently, they are acyclic over any pseudoconvex open subset of X.