PROJECTIVE BUNDLES ON INFINITE-DIMENSIONAL COMPLEX SPACES

Abstract. Let V be a complex localizing Banach space with countable un-conditional basis and E a rank r holomorphic vector bundle on P(V). Here we study the holomorphic embeddings of P(E) into products of projective spaces and the holomorphic line bundles on P(E). In particular we prove that if r ≥ 3, then H1(P(E), L) = 0 for every holomorphic line bundle L on P(E)