Isomorphic classification of the spaces of Whitney functions (Q1380992)

The authors consider the problem of isomorphic classification of spaces \({\mathcal E}(K)\) of infinitely differentiable Whitney functions on \(K\), when \(K\) is a compact set of the real line, with \(K\) equal to the closure of its interior. This is done via the linear topological invariant \(D_\varphi\) introduced by Vogt, Tidten, Goncharov and Zahariuta, and by the linear topological invariant \(\beta\) due to Goncharov and Zahariuta. The invariant \(D_\varphi\) is studied in Section II and the geometric linear topological invariant \(\beta\) in Section III. Although the two invariants are closely related, the authors give an example of a continuum of spaces \({\mathcal E}(K_\lambda)\) which cannot be distinguished by \(D_\varphi\) but which are shown to be pairwise nonisomorphic by means of \(\beta\).