Plurisubharmonic domination in Banach spaces

Details Plurisubharmonic domination in Banach spaces Plurisubharmonic domination in Banach spaces

2010-10-18

arxiv.org/abs/1010.3740v1

Mathematics

Complex Variables

7 pages

Scientific paper

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 $u(x)<\|h(x)\|$ for all $x\in\Omega$.

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