  The goal of this paper is to understand the properties of meromorphic
mappings with values in two model complex Hibert manifolds: Hilbert projective
space $\pp(l^2)$ and Sobolev loop space of the Riemann sphere $L\pp^1$. It
occurs that these properties are quite different. Based on our study we obtain
as a corollary that $L\pp^1$ does not admit a closed holomorphic imbedding to
$\pp(l^2)$. In other words $L\pp^1$ is {\slsf not} a Hilbert projective variety
despite of the fact that it is K\"ahler and meromorphic functions separate
points on it.
