[Généralisations de la propriété d'approximation de Haagerup pour les algèbres de von Neumann arbitraires]
La notion de propriété d'approximation de Haagerup, introduite à l'origine pour les algèbres de von Neumann ayant une trace finie, normale, et fidèle, est généralisée pour les algèbres de von Neumann arbitraires. Nous discutons deux caractérisations équivalentes : une du point de vue de la représentation standard et une autre du point de vue des applications linéaires approximantes liées à un poids fidèle, normal, semifini. Quelques propriétés de permanence, en particulier celles concernant les produits croisés, sont établies et certains exemples sont introduits.
The notion of the Haagerup approximation property, originally introduced for von Neumann algebras equipped with a faithful normal tracial state, is generalised to arbitrary von Neumann algebras. We discuss two equivalent characterisations, one in term of the standard form and the other in term of the approximating maps with respect to a fixed faithful normal semifinite weight. Several stability properties, in particular regarding the crossed product construction are established and certain examples are introduced.
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@article{CRMATH_2014__352_6_507_0,
author = {Caspers, Martijn and Okayasu, Rui and Skalski, Adam and Tomatsu, Reiji},
title = {Generalisations of the {Haagerup} approximation property to arbitrary von {Neumann} algebras},
journal = {Comptes Rendus. Math\'ematique},
pages = {507--510},
publisher = {Elsevier},
volume = {352},
number = {6},
year = {2014},
doi = {10.1016/j.crma.2014.04.003},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2014.04.003/}
}
TY - JOUR AU - Caspers, Martijn AU - Okayasu, Rui AU - Skalski, Adam AU - Tomatsu, Reiji TI - Generalisations of the Haagerup approximation property to arbitrary von Neumann algebras JO - Comptes Rendus. Mathématique PY - 2014 SP - 507 EP - 510 VL - 352 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2014.04.003/ DO - 10.1016/j.crma.2014.04.003 LA - en ID - CRMATH_2014__352_6_507_0 ER -
%0 Journal Article %A Caspers, Martijn %A Okayasu, Rui %A Skalski, Adam %A Tomatsu, Reiji %T Generalisations of the Haagerup approximation property to arbitrary von Neumann algebras %J Comptes Rendus. Mathématique %D 2014 %P 507-510 %V 352 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2014.04.003/ %R 10.1016/j.crma.2014.04.003 %G en %F CRMATH_2014__352_6_507_0
Caspers, Martijn; Okayasu, Rui; Skalski, Adam; Tomatsu, Reiji. Generalisations of the Haagerup approximation property to arbitrary von Neumann algebras. Comptes Rendus. Mathématique, Tome 352 (2014) no. 6, pp. 507-510. doi : 10.1016/j.crma.2014.04.003. http://www.numdam.org/articles/10.1016/j.crma.2014.04.003/
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