Plurisubharmonic domination in Banach spaces

Abstract

We show that if $X$ is a Banach space with a Schauder basis, $\Omega \subset X$ is a pseudoconvex open subset, and $u:\Omega \to (-\infty ,\infty )$ is a locally bounded function, then there are a Banach space $Z$ and a holomorphic function $h:\Omega \to Z$ with $u(x)<\Vert h(x)\Vert$ for all $x\in \Omega$.

7 pages