Interpolation of compact nonlinear operators
type: Item
instance of: scholarly article
title: Interpolation of compact nonlinear operators
zbMATH Open document ID: 0967.46020
DOI: 10.1155/S1025583400000126
published in: Journal of Inequalities and Applications
publication date: 2001-08-27T00:00:00Z
full work available at URL: https://eudml.org/doc/121178
review text: Let \((E_{0},E_{1})\) and \((F_{0},F_{1})\) be two Banach couples and let \(T:E_{0}+E_{1}\to F_{0}+F_{1}\) be a continuous map such that \(T:E_{0}\to F_{0}\) is a Lipschitz compact operator and \(T_{1}:E_{1}\to F_{1}\) is a Lipschitz operator. In this paper it is proved that if \(T:E_{1}\to F_{1}\) is also compact or \(E_{1}\) is continuously embedded in \(E_{0}\) or \(F_{1}\) is continuously embedded in \(F_{0}\), then \(T:(E_{0},E_{1})_{\theta, q}\to (F_{0},F_{1})_{\theta, q}\) is also a compact operator when \(1\leq q<\infty\) and \(0<\theta <1.\) Also the measure of non-compactness under real interpolation is investigated. The results of this paper extend some theorems of Cobos et al.
reviewed by: Nicolae Popa
Mathematics Subject Classification ID: 46B70
Mathematics Subject Classification ID: 46M35
zbMATH DE Number: 1507754
zbMATH Keywords: interpolation
zbMATH Keywords: compact nonlinear operators
zbMATH Keywords: measure of non-compactness
zbMATH Keywords: Lipschitz compact operator
author: António J. G. Bento
MaRDI profile type: Publication
OpenAlex ID: W2063975230
description: scientific article; zbMATH DE number 1507754