Semicompact operators
type: Item
instance of: scholarly article
title: Semicompact operators
zbMATH Open document ID: 0709.47023
DOI: 10.1016/0019-3577(90)90038-O
author: Anton R. Schep
author: Manfred P. H. Wolff
published in: Indagationes Mathematicae. New Series
publication date: 1990-01-01T00:00:00Z
review text: Let \({\mathcal S}^ r(E,F)\) (E and F are Banach lattices with F Dedekind complete) be the space of all regular operators T from E to F such that \(| T|\) maps norm bounded sets into almost order bounded once. As a followup to [\textit{W. Arendt} and \textit{H. U. Schwarz}, Math. Nachrichten 131, 7-18 (1987; Zbl 0641.47044)] this paper gives answers to the following problems: (a) When is \({\mathcal S}^ r(E,F)\) equal to the space of all regular operators? (b) When does \({\mathcal K}^ r(E,F)={\mathcal S}^ r(E,F)\cap (E'\otimes F)^{\perp \perp}\) hold? (c) When is \(E'\otimes F\) dense in \({\mathcal S}^ r(E,F)\) with respect to the r-norm? (d) When does \({\mathcal S}^ r(E,F)\) contain \((E'\otimes F)^{\perp \perp}?\)
Mathematics Subject Classification ID: 47B07
Mathematics Subject Classification ID: 47B65
Mathematics Subject Classification ID: 46B42
zbMATH DE Number: 4165785
zbMATH Keywords: Banach lattices
zbMATH Keywords: Dedekind complete
zbMATH Keywords: space of all regular operators
reviewed by: Joe Howard
MaRDI profile type: Publication
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full work available at URL: 0019-3577(90)90038-o
OpenAlex ID: W4205233327
description: scientific article; zbMATH DE number 4165785