Factoring compact operators and approximable operators
type: Item
instance of: scholarly article
title: Factoring compact operators and approximable operators
zbMATH Open document ID: 0744.47024
DOI: 10.4171/ZAA/397
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1992-06-25T00:00:00Z
review text: Let \(E\) be a Banach space, \(F\) be an ordered Banach space which belongs to a certain class of ordered spaces (say, Banach lattices). Let \(U: E\to F\) be a compact operator. The authors search for a factorization according to the scheme \(E @> U_ 1 >> G @> U_ 2 >> F\), where \(U_ 1\), \(U_ 2\) are compact operators and \(G\) is a reflexive ordered Banach space from a class which is as close as possible to those of \(F\). A modified version of the classical Davis-Figiel-Johnson-Pelczynski scheme is used. The article contains many interesting results. I would like only to mention that both, the problem of factorization and the problem of approximability, were under consideration in the reviewer's article [Soviet Math. Dokl. 17, 423-426 (1976; Zbl 0345.46011)] which is not quoted.
Mathematics Subject Classification ID: 47B60
Mathematics Subject Classification ID: 46B40
Mathematics Subject Classification ID: 47A68
zbMATH DE Number: 6502
zbMATH Keywords: ordered Banach space
zbMATH Keywords: Banach lattices
zbMATH Keywords: compact operator
zbMATH Keywords: factorization
zbMATH Keywords: compact operators
zbMATH Keywords: reflexive
zbMATH Keywords: Davis-Figiel-Johnson-Pelczynski scheme
zbMATH Keywords: approximability
author: Ioan Mircea Popovici
author: Dan Tudor Vuza
reviewed by: A. V. Bukhvalov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/zaa/397
OpenAlex ID: W2366279672
description: scientific article; zbMATH DE number 6502