Principle of local reflexivity for operators and quojections
type: Item
instance of: scholarly article
title: Principle of local reflexivity for operators and quojections
zbMATH Open document ID: 0673.46002
DOI: 10.1007/BF01188686
published in: Archiv der Mathematik
publication date: 1990-01-01T00:00:00Z
review text: The principle of local reflexivity for linear operators between Banach spaces is proved. Then it is applied in order to obtain the principle for locally convex (especially Fréchet) spaces X whenever X is a quojection. A special dual form of the principle for strict LB-spaces is also obtained. The results of the paper are applied in order to generalize the theory of \({\mathcal L}_ p\)-spaces to the classes of Fréchet and strict LB-spaces in the author's paper: ``\({\mathcal L}_ p\)- and injective locally convex spaces'', Dissertationes Math., to appear.
Mathematics Subject Classification ID: 46A04
Mathematics Subject Classification ID: 46A13
Mathematics Subject Classification ID: 46A11
Mathematics Subject Classification ID: 46A20
Mathematics Subject Classification ID: 46B10
Mathematics Subject Classification ID: 46A03
Mathematics Subject Classification ID: 47A05
zbMATH DE Number: 4101853
zbMATH Keywords: Frechet spaces
zbMATH Keywords: locally convex space
zbMATH Keywords: Script \(L_ p\)-space
zbMATH Keywords: principle of local reflexivity for linear operators between Banach spaces
zbMATH Keywords: quojection
zbMATH Keywords: strict LB-spaces
author: Paweł Domański
MaRDI profile type: Publication
cites work: Q3749573
cites work: On the principle of local reflexivity
cites work: Normal operators and multipliers on complex Banach spaces and a symmetry property of \(L^ 1\)-predual spaces
cites work: On a problem of Bellenot and Dubinsky
cites work: General principle of local reflexivity in the theory of cone duality
cites work: A note on quojections
cites work: A note on strictly regular Fréchet spaces
cites work: Weakly unconditionally convergent series in M-ideals.
cites work: On bases, finite dimensional decompositions and weaker structures in Banach spaces
cites work: The \(L_ p\) spaces
cites work: Q4727658
cites work: Q3756005
cites work: Strictly regular Frechet spaces
full work available at URL: https://doi.org/10.1007/bf01188686
OpenAlex ID: W2023618672
description: scientific article; zbMATH DE number 4101853