(\(p\),\(q\))-summing sequences
type: Item
instance of: scholarly article
title: (\(p\),\(q\))-summing sequences
zbMATH Open document ID: 1010.46014
DOI: 10.1016/S0022-247X(02)00379-7
author: Oscar Blasco
author: José Luis Arregui
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-02-11T00:00:00Z
review text: The authors consider the spaces formed by \((p, q)\)-summing sequences relating them to the theory of \((p, q)\)-summing operators. They give a characterization of the special case \(p = 1\) in terms of integral operators and show how these spaces are relevant for a general question on Banach spaces and their duals. Indeed, they give a formulation of the Grothendieck theorem that gives a partial answer to a question about the way that bounded sequences in the dual space \(X^*\) interact with bounded sequences in the space \(X\).
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46B03
Mathematics Subject Classification ID: 47B10
zbMATH DE Number: 1866661
zbMATH Keywords: sequences on Banach spaces
zbMATH Keywords: (p, q)-summing operators
zbMATH Keywords: type and cotype
zbMATH Keywords: Grothendieck theorem
zbMATH Keywords: weak principle of local reflexivity
reviewed by: Ganesh Datta Dikshit
MaRDI profile type: Publication
cites work: On summing multipliers and applications
cites work: Q4850055
cites work: Q3995204
cites work: Q4023934
cites work: Cotype of operators from \(C(K)\)
cites work: Cotype and \((q,1)\)-summing norm in a Banach space
cites work: Some remarks on (p,q)-absolutely summing operators in $l_{p}$-spaces
full work available at URL: s0022-247x(02)00379-7
OpenAlex ID: W1989170458
description: scientific article; zbMATH DE number 1866661