Vogt, Dietmar Spaces of Whitney jets on self-similar sets. (English) Zbl 1316.46024 Stud. Math. 218, No. 1, 89-94 (2013). Let \(E\) be a complemented subspace of the Fréchet space \(s\). The author gives a sufficient condition under which \(E\) is isomorphic to \(s\).More 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 [A. Aytuna et al., Math. Ann. 283, No. 2, 193–202 (1989; Zbl 0643.46001)].This 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. Reviewer: Michał Goliński (Poznań) MSC: 46E10 Topological linear spaces of continuous, differentiable or analytic functions 46A04 Locally convex Fréchet spaces and (DF)-spaces 46A63 Topological invariants ((DN), (\(\Omega\)), etc.) for locally convex spaces Keywords:Whitney jets; space \(s\); Cantor set; Sierpiński triangle; self-similar set Citations:Zbl 0643.46001 PDFBibTeX XMLCite \textit{D. Vogt}, Stud. Math. 218, No. 1, 89--94 (2013; Zbl 1316.46024) Full Text: DOI Link