On the non-nuclearity of a space of test functions on Hilbert space
type: Item
instance of: scholarly article
title: On the non-nuclearity of a space of test functions on Hilbert space
zbMATH Open document ID: 0831.46042
author: Rod Donnelly
published in: Journal of Functional Analysis
publication date: 1996-02-18T00:00:00Z
review text: \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.
Mathematics Subject Classification ID: 46F25
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 46A11
zbMATH DE Number: 764010
zbMATH Keywords: infinitely differentiable functions with bounded support on a real separable Hilbert space
zbMATH Keywords: space of generalized measures
zbMATH Keywords: non-nuclearity of Dudin's space
MaRDI profile type: Publication
full work available at URL: jfan.1995.1033
OpenAlex ID: W2000690550
DOI: 10.1006/JFAN.1995.1033
description: scientific article; zbMATH DE number 764010