A characteristic property of the space s

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 $s$, so completing the theory developed in "Restriction spaces of $A^{\infty }$", to appear in Rev. Mat. Iberoamericana 29.4 (2013)

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