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

Author(s): Dietmar Vogt
Journal: Proc. Amer. Math. Soc. 138 (2010), 1421-1423.
MSC (2010): Primary 46A04; Secondary 46A11
Posted: November 3, 2009
MathSciNet review: 2578534
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Abstract | References | Similar articles | Additional information

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 $\mathbb{R}^3$ .

References:

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3.: Dubinsky, E., Vogt, D., Fréchet spaces with quotients failing the bounded approximation property, Studia Math. 81 (1985), 71-77. MR 818172 (87e:46005)
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5.: Meise, R., Vogt, D., Introduction to functional analysis, The Clarendon Press, Oxford Univ. Press, New York, 1997. MR 1483073 (98g:46001)
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7.: Vogt, D., An example of a nuclear Fréchet space without the bounded approximation property, Math. Z. 182 (1983), 265-267. MR 689304 (84m:46009)
8.: Vogt, D., A nuclear Fréchet space of $C^\infty$ -functions which has no basis, Note Mat. 25 (2005/06), 187-190. MR 2259965 (2007g:46004)

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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: 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
Posted: November 3, 2009
Communicated by: Nigel J. Kalton
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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