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Plurisubharmonic domination

Author: László Lempert
Journal: J. Amer. Math. Soc. 17 (2004), 361-372
MSC (2000): Primary 32Txx, 32U05, 46G20
Published electronically: November 25, 2003
MathSciNet review: 2051614
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Abstract: For a large class of separable Banach spaces $X$ we prove the following. Given a pseudoconvex open $\Omega \subset X$ and $u:\Omega\to\mathbb{R}$ that is locally bounded above, there is a plurisubharmonic $v:\Omega\to\mathbb{R}$ such that $u\le v$. We also discuss applications of this result.

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Additional Information

László Lempert
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

Received by editor(s): March 6, 2003
Published electronically: November 25, 2003
Additional Notes: Research partially supported by an NSF grant
Article copyright: © Copyright 2003 American Mathematical Society