The closed ideal of \((c_0, p, q)\)-summing operators
type: Item
instance of: scholarly article
title: The closed ideal of \((c_0, p, q)\)-summing operators
zbMATH Open document ID: 0981.47018
DOI: 10.1007/BF01291716
author: Aicke Hinrichs
author: Albrecht Pietsch
published in: Integral Equations and Operator Theory
publication date: 2001-01-25T00:00:00Z
review text: The authors study the closed operator ideal formed by the \((c_0,p,q)\)-summing operators, provided that \(1/p+ 1/q\leq 1\). The identity map \(Id: \ell_{p^*}\to \ell_q\) factors through \(T: X\to Y\) if and only if \(T\) does not belong to this ideal. The associated superideal consists of those maps \(T\) for which all ultrapowers belong to the class of \((c_0,p,q)\)-summing operators. Operators in the complement of this superideal factor the identity maps \(Id: \ell^n_{p^*}\to \ell^n_q\) uniformly.
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 47L20
Mathematics Subject Classification ID: 46B28
Mathematics Subject Classification ID: 46B07
zbMATH DE Number: 1556616
zbMATH Keywords: ultrapowers
zbMATH Keywords: fractorization
zbMATH Keywords: closed operator ideal
zbMATH Keywords: \((c_0,p,q)\)-summing operators
zbMATH Keywords: associated superideal
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01291716
OpenAlex ID: W2086164695
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description: scientific article; zbMATH DE number 1556616