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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Stein spaces characterized by their endomorphisms


Author: Rafael B. Andrist
Journal: Trans. Amer. Math. Soc. 363 (2011), 2341-2355
MSC (2000): Primary 32E10, 32M10; Secondary 20M20, 54H15
Published electronically: November 23, 2010
MathSciNet review: 2763719
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Abstract: Finite-dimensional Stein spaces admitting a proper holomorphic embedding of the complex line are characterized, among all complex spaces, by their holomorphic endomorphism semigroup in the sense that any semigroup isomorphism induces either a biholomorphic or an antibiholomorphic map between them.


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Additional Information

Rafael B. Andrist
Affiliation: Mathematisches Institut, Universität Bern, Sidlerstr. 5, 3012 Bern, Switzerland
Email: rafael.andrist@math.unibe.ch

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05104-9
PII: S 0002-9947(2010)05104-9
Keywords: Holomorphic endomorphism, Stein space, semigroup, density property
Received by editor(s): September 23, 2008
Published electronically: November 23, 2010
Additional Notes: This work was partially supported by Schweizerischer Nationalfonds grant no. 200021-116165
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.