Isomorphic classification of the spaces of Whitney functions
type: Item
instance of: scholarly article
title: Isomorphic classification of the spaces of Whitney functions
zbMATH Open document ID: 0931.46019
author: Alexander Goncharov
author: Mefharet Kocatepe
published in: Michigan Mathematical Journal
publication date: 2000-02-23T00:00:00Z
review text: 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 \(\beta\).
Mathematics Subject Classification ID: 46E10
Mathematics Subject Classification ID: 46A63
Mathematics Subject Classification ID: 46T20
zbMATH DE Number: 1127772
zbMATH Keywords: Whitney functions
zbMATH Keywords: isomorphic classification of Fréchet spaces
zbMATH Keywords: linear topological invariant
reviewed by: João B. Prolla
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029005788
OpenAlex ID: W2044579417
DOI: 10.1307/MMJ/1029005788
description: scientific article; zbMATH DE number 1127772