A characteristic property of the space s

Original · EN

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∞(X) of restrictions to X of C∞-functions on is isomorphic to s, so completing the theory developed in "Restriction spaces of A∞", to appear in Rev. Mat. Iberoamericana 29.4 (2013)