Topologically trivial holomorphic vector bundles on infinite-dimensional projective varieties

Abstract

Let V be an infinite-dimensional locally convex complex space, X a closed subset of P(V) defined by finitely many continuous homogeneous equations and E a holomorphic vector bundle on X with finite rank. Here we show that E is holomorphically trivial if it is topologically trivial and spanned by its global sections and in a few other cases.