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A characteristic property of the space $ s$


Author: Dietmar Vogt
Journal: Proc. Amer. Math. Soc. 143 (2015), 1183-1187
MSC (2010): Primary 46A45, 46A63, 46E10
DOI: https://doi.org/10.1090/S0002-9939-2014-12320-3
Published electronically: November 4, 2014
MathSciNet review: 3293733
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Abstract: It is shown that under certain stability conditions a complemented subspace of the space $ s$ of rapidly decreasing sequences is isomorphic to $ s$ and this condition characterizes $ s$. This result is used to show that, for the classical Cantor set $ X$, the space $ C_\infty (X)$ of restrictions to $ X$ of $ C^\infty $-functions on $ \mathbb{R}$ is isomorphic to $ s$, which leads to an improvement of the theory developed in a previous work of the author.


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Additional Information

Dietmar Vogt
Affiliation: FB Math.-Nat., Bergische Universität Wuppertal, Gauß-Str. 20, 42119 Wuppertal, Germany
Email: dvogt@math.uni-wuppertal.de

DOI: https://doi.org/10.1090/S0002-9939-2014-12320-3
Keywords: Space $s$, stability condition, Cantor set
Received by editor(s): May 16, 2013
Received by editor(s) in revised form: July 10, 2013
Published electronically: November 4, 2014
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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