Let (E, ‖ ‖) be a complex normed space, E' its dual and B₁ ⊂ E' the dual of the unit ball of E. Equip E' and hence B₁ with the weak*-topology σ(E, E'), but call E'_k the space E' with the kelleyfication topology of σ(E, E') and use the corresponding complex structure. Here we prove that   for every q ≥ 2 and   for every i ≥ 1. Let M be a complex manifold locally modelled over an infinite-dimensional Banach space with countable unconditional basis and with the localizing property. Let S ⊂ M be a discrete subset and E a locally free sheaf on M with finite rank. Here we prove that the natural map   is bijective.