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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

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
Email: lempert@math.purdue.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-03-00448-X
PII: S 0894-0347(03)00448-X
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