A characteristic property of the space 𝑠

Vogt, Dietmar

doi:10.1090/S0002-9939-2014-12320-3

A characteristic property of the space $s$
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by Dietmar Vogt

Proc. Amer. Math. Soc. 143 (2015), 1183-1187

DOI: https://doi.org/10.1090/S0002-9939-2014-12320-3

Published electronically: November 4, 2014

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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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