On the lifting property for \(C^{\ast}\)-algebras
type: Item
instance of: scholarly article
title: On the lifting property for \(C^{\ast}\)-algebras
DOI: 10.4171/JNCG/473
author: Gilles Pisier
published in: Journal of Noncommutative Geometry
publication date: 2022-12-08T00:00:00Z
review text: Summary: We characterize the lifting property (LP) of a separable \(C^{\ast}\)-algebra \(A\) by a property of its maximal tensor product with other \(C^{\ast}\)-algebras, namely we prove that \(A\) has the LP of and only if for any family \(\{D_i \mid i \in I\}\) of \(C^{\ast}\)-algebras the canonical map \(\ell_{\infty}(\{D_i\}) \oplus_{\max} A \to \ell_{\infty}(\{D_i \oplus_{\max} A\})\) is isometric. Equivalently, this holds if and only if \(M \oplus_{\max} A = M \oplus_{\mathrm{nor}} A\) for any von Neumann algebra \(M\).
Mathematics Subject Classification ID: 46L06
Mathematics Subject Classification ID: 46L07
Mathematics Subject Classification ID: 46L09
zbMATH DE Number: 7629322
zbMATH Keywords: \(C^{\ast}\)-algebras
zbMATH Keywords: von Neumann algebras
zbMATH Keywords: lifting property
zbMATH Keywords: tensor products
Wikidata QID: Q114021466
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7629322