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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A nuclear Fréchet space consisting of $ C^\infty$-functions and failing the bounded approximation property


Author: Dietmar Vogt
Journal: Proc. Amer. Math. Soc. 138 (2010), 1421-1423
MSC (2010): Primary 46A04; Secondary 46A11
Published electronically: November 3, 2009
MathSciNet review: 2578534
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Abstract: An easy and transparent example is given of a nuclear Fréchet space failing the bounded approximation property and consisting of $ C^\infty$-functions on a subset of $ \mathbb{R}^3$.


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Additional Information

Dietmar Vogt
Affiliation: Fachbereich C–Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, D-42097 Wuppertal, Germany
Email: dvogt@math.uni-wuppertal.de

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10166-1
PII: S 0002-9939(09)10166-1
Received by editor(s): January 11, 2009
Received by editor(s) in revised form: August 13, 2009
Published electronically: November 3, 2009
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.