\(L_ \varphi\)-spaces and some related sequence spaces
type: Item
instance of: scholarly article
title: \(L_ \varphi\)-spaces and some related sequence spaces
zbMATH Open document ID: 0807.46007
DOI: 10.4171/ZAA/507
author: Karl-Goswin Grosse-Erdmann
author: Johann Boos
author: Toivo Leiger
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1994-09-01T00:00:00Z
review text: Summary: In view of closed graph theorems in case of maps defined by operator- valued matrices \(L_ \varphi\)-spaces were recently introduced by two of the present authors as a generalization of separable \(FK(X)\)-spaces. In this paper we study the class of \(L_ \varphi\)-spaces and a few closely related classes of sequence spaces. It is shown that an analogue of Kalton's closed graph theorem holds for matrix mappings if we consider \(L_ \varphi\)-spaces as range spaces, and paralleling a result of Qiu we prove that the class of \(L_ \varphi\)-spaces is the best-possible choice here. As a consequence we show that for any \(L_ \varphi\)-space \(E\) every matrix domain \(E_ A\) is again an \(L_ \varphi\)-space.
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 46A30
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 40H05
zbMATH DE Number: 627641
zbMATH Keywords: \(L_ r\)-spaces
zbMATH Keywords: maps defined by operator-valued matrices
zbMATH Keywords: Kalton's closed graph theorem
zbMATH Keywords: matrix mappings
zbMATH Keywords: \(L_ \varphi\)-spaces
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 627641