Multilinear extensions of absolutely \((p;q;r)\)-summing operators
type: Item
instance of: scholarly article
title: Multilinear extensions of absolutely \((p;q;r)\)-summing operators
zbMATH Open document ID: 1238.46040
author: Dahmane Achour
publication date: 2012-02-09T00:00:00Z
review text: The author introduces and explores the notion of absolutely \(\left( p;q_{1},\dots,q_{m};r\right) \)-summing multilinear operators. When \(r=\infty\) the well-known case of absolutely \(\left( p;q_{1},\dots,q_{m}\right) \)-summing multilinear operators is recovered. Among several interesting results, a Pietsch domination-type theorem is proved. The proof uses a general technique introduced by the reviewer, \textit{J. Santos} and \textit{J. B. Seoane-Sepúlveda} [Adv. Math. 229, No. 2, 1235--1265 (2012; Zbl 1248.47024)]. A factorization theorem and connections with the class of Cohen strongly \(p\)-summing multilinear operators are also presented.
Mathematics Subject Classification ID: 46G25
Mathematics Subject Classification ID: 47L22
Mathematics Subject Classification ID: 47L20
Mathematics Subject Classification ID: 46A32
zbMATH DE Number: 6004389
zbMATH Keywords: absolutely summing operators
zbMATH Keywords: absolutely summing multilinear operators
zbMATH Keywords: Pietsch domination theorem
reviewed by: Daniel Pellegrino
MaRDI profile type: Publication
full work available at URL: s12215-011-0054-2
OpenAlex ID: W2019677782
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DOI: 10.1007/S12215-011-0054-2
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 6004389