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arXiv · 1304.3820

A characteristic property of the space s

Dietmar Vogt
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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 $\R$ is isomorphic to $s$, so completing the theory developed in "Restriction spaces of $A^\infty$", to appear in Rev. Mat. Iberoamericana 29.4 (2013)

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Dietmar Vogt. 2013-04-13. A characteristic property of the space s. https://arxiv.org/abs/1304.3820

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