Mappings between Banach spaces that send mixed summable sequences into absolutely summable sequences
type: Item
instance of: scholarly article
title: Mappings between Banach spaces that send mixed summable sequences into absolutely summable sequences
zbMATH Open document ID: 1067.47029
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-10-12T00:00:00Z
review text: This paper deals with a generalization of the notion of \((p,q)\)-summing operators on a Banach space that was introduced by Pietsch and studied by him and numerous others many years ago. The definitions as well as the results obtained are highly technical and consequently will not be summarized here. A quote from the author's abstract will suffice to indicate the nature and direction of the work. ``We study mappings from an open subset \(A\) of a Banach space \(E\) into another Banach space \(F\) such that, once \(a\) in \(A\) is fixed, for mixed \((s;q)\)-summable sequences \(\{x(j)\}\) of elements of a fixed neighborhood of \(0\) in \(E\), the sequence \(\{f(a+ x(j))- f(a)\}\) is absolutely \(p\)-summable in \(F\).''
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 47H60
zbMATH DE Number: 2107223
zbMATH Keywords: absolutely summable
zbMATH Keywords: \((p,q)\)-summability
author: Mário Carvalho Matos
reviewed by: James R. Holub
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.06.020
OpenAlex ID: W2022359592
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DOI: 10.1016/J.JMAA.2004.06.020
description: scientific article; zbMATH DE number 2107223