Some properties of the space of regular operators on atomic Banach lattices
type: Item
instance of: scholarly article
title: Some properties of the space of regular operators on atomic Banach lattices
zbMATH Open document ID: 1225.46013
author: Qingying Bu
author: Yongjin Li
author: Xiaoping Xue
published in: Collectanea Mathematica
publication date: 2011-06-22T00:00:00Z
review text: Let \(L^{r}(E,X)\) denote the space of all regular linear operators from a Banach lattice \(E\) to a Banach lattice \(X\). In this paper among other things the authors show that if \(E\) is a separable atomic Banach lattice, then \(L^{r}(E,X)\) is reflexive if and only if both \(E\) and \(X\) are reflexive and each positive linear operator from \(E\) into \(X\) is compact.
reviewed by: Ömer Gök
Mathematics Subject Classification ID: 46B28
Mathematics Subject Classification ID: 46B42
Mathematics Subject Classification ID: 47B65
zbMATH DE Number: 5911548
zbMATH Keywords: Banach lattices
zbMATH Keywords: space of regular operators
zbMATH Keywords: reflexivity
zbMATH Keywords: Radon-Nikodym property
MaRDI profile type: Publication
full work available at URL: s13348-010-0007-7
OpenAlex ID: W1996224296
cites work: Schauder decompositions and the Fremlin projective tensor product of Banach lattices
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cites work: Q4039882
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cites work: Schauder Decompositions and Completeness
cites work: Q4136031
cites work: Banach lattices
DOI: 10.1007/S13348-010-0007-7
description: scientific article; zbMATH DE number 5911548