On a pseudoconvex domain spread over a complex projective space induced from a complex Banach space with a Schauder basis (Q1097991)

The author proves two results on infinite-dimensional complex manifolds having their sources in the Levi problem and the imbedding theorem for Stein manifolds. The first theorem gives equivalent conditions for a domain (\(\Omega\),\(\phi)\) spread over a projective space of a complex Banach space with Schauder basis to be a domain of holomorphy. The second theorem states that for a pseudoconvex domain (\(\Omega\),\(\phi)\) spread over a projective space of a separable Hilbert space H, there is a holomorphic injection f of \(\Omega\) into H, such that the restriction of f to certain finite-dimensional subspaces of \(\Omega\) is regular and proper.