On reiteration and the behaviour of weak compactness under certain interpolation methods
type: Item
instance of: scholarly article
title: On reiteration and the behaviour of weak compactness under certain interpolation methods
zbMATH Open document ID: 0935.46060
published in: Collectanea Mathematica
publication date: 2000-05-04T00:00:00Z
full work available at URL: https://eudml.org/doc/42601
review text: This article deals with K- and J-spaces defined by means of polygons. First, we establish some reiteration formulae involving the real method, and then we study the behaviour of weakly compact operators. We show that if just one restriction of the operator \(T\) is weakly compact, then the interpolation operator from a J-space into a K-space also has this property, but in general this is not the case if we consider \(T\) acting between two J-spaces or two K-spaces. For these cases we prove that the interpolated operator is weakly compact provided that all but two restrictions of \(T\) (located in adjacent vertices of the polygon) are weakly compact. We also show by means of examples that these results are best possible.
Mathematics Subject Classification ID: 46M35
Mathematics Subject Classification ID: 46B70
Mathematics Subject Classification ID: 47B07
zbMATH DE Number: 1383045
zbMATH Keywords: means of polygons
zbMATH Keywords: reiteration formulae
zbMATH Keywords: weakly compact operators
zbMATH Keywords: interpolation operator from a J-space into a K-space
author: Fernando Cobos
author: Pedro Fernández-Martínez
author: Antón Martínez
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1383045