On the non-nuclearity of a space of test functions on Hilbert space
\textit{D. N. Dudin} [Trans. Mosc. Math. Soc. 28(1973), 133-157 (1975; Zbl 0295.46061)] has constructed a space \({\mathcal D}({\mathcal H})\), consisting of all the infinitely differentiable functions with bounded support on a real separable Hilbert space \(\mathcal H\), all of whose derivatives have bounded range. He establishes that \({\mathcal D}'({\mathcal H})\), the dual of \({\mathcal D}({\mathcal H})\), can be identified with a certain space of generalized measures. In this work the author establishes the non-nuclearity of Dudin's space \({\mathcal D}({\mathcal H})\). The result follows by modifying a result of Meise that a certain space of infinitely differentiable functions on a real locally convex space, not necessarily of bounded support, is non-nuclear.
infinitely differentiable functions with bounded support on a real separable Hilbert space
scientific article; zbMATH DE number 764010