An Embedding Theorem for Pseudoconvex Domains in Banach Spaces

We show that a pseudoconvex open subset of a Banach space with an unconditional basis is biholomorphic to a closed direct submanifold of a Banach space with an unconditional basis.This research supported in part by NSF grant DMS-0203072 and a Bilsland Dissertation Fellowship from the Graduate School of Purdue University. This paper is the result of my thesis research under the direction of László Lempert, and I would like to thank him for his patient and wise guidance. I would also like to thank Andreas Defant and David Pérez-García for their suggestions regarding tensor products and directing me to the paper [4], and Steve Bell for his suggestions.