A compactness criterion of mixed Krasnoselskiĭ-Riesz type in regular ideal spaces of vector functions
type: Item
instance of: scholarly article
title: A compactness criterion of mixed Krasnoselskiĭ-Riesz type in regular ideal spaces of vector functions
zbMATH Open document ID: 0941.46016
DOI: 10.4171/ZAA/908
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1999-12-20T00:00:00Z
full work available at URL: https://eudml.org/doc/48480
review text: There is given a compactness criterion in ideal spaces (Banach function spaces) of vector-valued functions \(f\) on a measure space \(S\), with values in a Banach space \(U\). It follows from some estimates between measures of non-compactness \(\alpha\) of Kuratowski, \(\chi_Y\) by Hausdorff, \(\chi_i=\) inner Hausdorff measure of non-compactness, and a measure \(\omega\). If \(X\) is a regular preideal space (Köthe space) of functions \(f: S\to U\), where \(U\) is finite-dimensional, from these estimates follow necessary and sufficient conditions in order that \(M\subset X\) be precompact.
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46B50
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 46G10
zbMATH DE Number: 1356405
zbMATH Keywords: Köthe space
zbMATH Keywords: compactness criterion
zbMATH Keywords: ideal spaces
zbMATH Keywords: Hausdorff measure of non-compactness
zbMATH Keywords: preideal space
author: Martin Väth
reviewed by: Julian Musielak
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1356405