Spaces of Whitney jets on self-similar sets (Q2856672)

Let \(E\) be a complemented subspace of the Fréchet space \(s\). The author gives a sufficient condition under which \(E\) is isomorphic to \(s\).NEWLINENEWLINEMore precisely, if a normwise exact sequence \(0 \to E \to E \oplus \ldots \oplus E \to G \to 0\) exists (for \(G=\{0\}\) or \(G=\omega\)), then the Kolmogorov diameters of the local Banach spaces of \(E\) can be estimated and the isomorphism follows by a result in [\textit{A. Aytuna} et al., Math. Ann. 283, No. 2, 193--202 (1989; Zbl 0643.46001)].NEWLINENEWLINEThis condition is applied to spaces of Whitney jets on the Cantor set and on the Sierpiński triangle. The results can probably be extended to other self-similar sets.