Tame spaces and power series spaces
type: Item
instance of: scholarly article
title: Tame spaces and power series spaces
zbMATH Open document ID: 0622.46004
DOI: 10.1007/BF01160894
author: Dietmar Vogt
published in: Mathematische Zeitschrift
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173901
review text: For tame Fréchet spaces in the sense of \textit{R. S. Hamilton}, [Bull. Am. Math. Soc. 7, 65-222 (1982; Zbl 0499.58003)] or \textit{F. Sergeraert} [Ann. Sci. Éc. Norm. Sup., IV Sér. 5, 599-660 (1972; Zbl 0246.58006)] we prove the following theorems: I. Theorem: If \(0\to F\to G\to ^{q}H\to 0\) is a tame exact sequence of tame Fréchet spaces, one of which is nuclear, then it splits tamely, i.e. q has a tame right inverse. II. Theorem: Every nuclear tame Fréchet space is tamely equivalent to a power series space of infinite type.
Mathematics Subject Classification ID: 46A13
Mathematics Subject Classification ID: 46A11
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 46A04
zbMATH DE Number: 4009066
zbMATH Keywords: tame Fréchet spaces
zbMATH Keywords: exact sequence of tame Fréchet spaces
zbMATH Keywords: tame right inverse
zbMATH Keywords: every nuclear tame Fréchet space is tamely equivalent to a power series space of infinite type
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4009066