A sufficient condition for vanishing of the derived projective limit functor
type: Item
instance of: scholarly article
title: A sufficient condition for vanishing of the derived projective limit functor
zbMATH Open document ID: 0859.46046
DOI: 10.1007/BF01197593
author: Jochen Wengenroth
author: Leonhard Frerick
published in: Archiv der Mathematik
publication date: 1997-04-07T00:00:00Z
review text: In 1968, V. P. Palamodov developed the theory of the projective limit functor in the category of locally convex spaces and introduced the derived projective limit functor Proj\(^1\) as a tool for investigating surjectivity problems in various parts of analysis (e.g. solvability of partial differential equations). He and V. S. Retakh obtained a characterization of Proj\(^1=0\) in terms of linear topological properties of the spaces forming the projective spectrum, which has been applied also recently e.g. by R. Braun, R. Meise and D. Vogt to describe surjectivity of convolution operators on classes of ultradifferentiable functions and by Vogt to the splitting theory for Fréchet spaces. For these applications one condition in Palamodov's and Retakh's characterization is very difficult to check. The paper under review contains as the main result a sufficient condition for Proj\(^1=0\) which fits better in the situations mentioned above. Using this new condition a characterization of the splitting relation for large classes of Fréchet spaces is given which completes results of Vogt.
reviewed by: Jochen Wengenroth
Mathematics Subject Classification ID: 46M15
Mathematics Subject Classification ID: 46A13
Mathematics Subject Classification ID: 46A04
zbMATH DE Number: 938606
zbMATH Keywords: projective limit functor
zbMATH Keywords: category of locally convex spaces
zbMATH Keywords: projective spectrum
zbMATH Keywords: surjectivity of convolution operators
zbMATH Keywords: splitting theory for Fréchet spaces
zbMATH Keywords: Fréchet spaces
MaRDI profile type: Publication
cites work: Existence of Fundamental Solutions and Surjectivity of Convolution Operators on Classes of Ultra-Differentiable Functions
cites work: Q4355968
cites work: The splitting relation for Köthe spaces
cites work: Q5565435
cites work: Acyclic inductive spectra of Fréchet spaces
full work available at URL: https://doi.org/10.1007/bf01197593
OpenAlex ID: W2063080683
description: scientific article; zbMATH DE number 938606