Restrictions of unbounded continuous linear operators on Fréchet spaces
type: Item
instance of: scholarly article
title: Restrictions of unbounded continuous linear operators on Fréchet spaces
zbMATH Open document ID: 0578.46002
DOI: 10.1007/BF01195024
author: M. Yurdakul
author: A. Tosun Terz{i}oğlu
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: It is proved that if E is a Fréchet space, F a closed subspace of a Fréchet space \(F_ 1\) which has a basis and admits a continuous norm and \(T: E\to F\) is a continuous unbounded linear operator, then there is an infinite-dimensional closed nuclear subspace G of E which has a basis such that the restriction of T to G is an isomorphism onto T(G). In the proof, a modification of a result of Bessaga, Pelczynski and Rolewicz, which was employed to construct a nuclear subspace of a Fréchet space is used.
Mathematics Subject Classification ID: 46A13
Mathematics Subject Classification ID: 46A11
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 46A04
zbMATH DE Number: 3925540
zbMATH Keywords: basic sequences
zbMATH Keywords: continuous norm
zbMATH Keywords: continuous unbounded linear operator
zbMATH Keywords: nuclear subspace of a Fréchet space
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01195024
OpenAlex ID: W1970390700
description: scientific article; zbMATH DE number 3925540