A sufficient condition for \(\text{Proj}^1\chi=0\)
type: Item
instance of: scholarly article
title: A sufficient condition for \(\text{Proj}^1\chi=0\)
zbMATH Open document ID: 0901.46062
author: Rüdiger W. Braun
author: Dietmar Vogt
published in: Michigan Mathematical Journal
publication date: 1998-09-15T00:00:00Z
review text: Given a countable projective spectrum \({\mathcal X}=(X_k)\) of topological vector spaces, \textit{V. P. Palamodov} [Mat. Sb. (N.S.) 75(117), 567-603 (1968; Zbl 0175.41801)] introduced a functor \(\text{Proj}^1{\mathcal X}\). For the case where each \(X_k\) is an inductive limit of Banach spaces (with some compatibility condition), the authors prove a sufficient condition for \(\text{Proj}^1{\mathcal X}=0\) [see also \textit{L. Frerick} and \textit{J. Wengenroth}, Arch. Math. 67, No. 4, 296-301 (1996; Zbl 0859.46046)]. If the \(X_k\) are DFS-spaces, this condition is shown to be necessary as well. Applications to partial differential operators are sketched.
Mathematics Subject Classification ID: 46M15
Mathematics Subject Classification ID: 46A13
zbMATH DE Number: 1046973
zbMATH Keywords: projective limits
zbMATH Keywords: homology
zbMATH Keywords: DFS-spaces
zbMATH Keywords: countable projective spectrum
zbMATH Keywords: functor
zbMATH Keywords: partial differential operators
reviewed by: V. Losert
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029005626
OpenAlex ID: W2031157387
DOI: 10.1307/MMJ/1029005626
description: scientific article; zbMATH DE number 1046973