Comparison of non-commutative 2- and \(p\)-summing operators from \(B(l_2)\) into \(OH\)
type: Item
instance of: scholarly article
title: Comparison of non-commutative 2- and \(p\)-summing operators from \(B(l_2)\) into \(OH\)
zbMATH Open document ID: 1018.46030
DOI: 10.4171/ZAA/1104
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2003-09-11T00:00:00Z
review text: Summary: In the theory of \(p\)-summing operators studied by Pietsch we know that \[ \pi_2(C(K),H)= \pi_p(C(K), H) \] for any Hilbert space \(H\) and any \(p\) such that \(2<p<+ \infty\). In this paper, we prove that this equality is not true for the same notion generalized by Junge and Pisier to operator spaces, i.e., \(\pi_{l_2} (B(l_2),OH) (=\pi_2^0(B(l_2),OH)) \neq\pi_{l_p} (B(l_2), OH)\).
Mathematics Subject Classification ID: 46L07
Mathematics Subject Classification ID: 46B28
Mathematics Subject Classification ID: 47B10
zbMATH DE Number: 1827607
zbMATH Keywords: operator spaces
zbMATH Keywords: completely bounded operators
author: Lahcène Mezrag
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1827607