(F)-spaces and strict (LF)-spaces
type: Item
instance of: scholarly article
title: (F)-spaces and strict (LF)-spaces
zbMATH Open document ID: 0628.46001
DOI: 10.1007/BF01161761
published in: Mathematische Zeitschrift
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/183697
review text: Some results about the existence of certain quotient spaces of some classes of Köthe echelon spaces are proved. These are used to relate the concepts of B- and \(B_ r\)-completeness, which were introduced by Pták, and the existence of (locally) complete quotient spaces for strict (LF)-spaces and their duals. The results are then applied to prove that the space of ultradifferentiable functions and the space of ulradistributions of Beurling are not \(B_ r\)-complete.
Mathematics Subject Classification ID: 46A04
Mathematics Subject Classification ID: 46A13
Mathematics Subject Classification ID: 46A11
Mathematics Subject Classification ID: 46A30
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 46F05
zbMATH DE Number: 4021875
zbMATH Keywords: existence of certain quotient spaces of some classes of Köthe echelon spaces
zbMATH Keywords: B- and \(B_ r\)-completeness
zbMATH Keywords: (locally) complete quotient spaces for strict (LF)-spaces and their duals
zbMATH Keywords: space of ultradifferentiable functions and the space of ulradistributions of Beurling are not \(B_ r\)-complete
author: Manuel Valdivia
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4021875