TY - JOUR
T1 - Generalisations of the Haagerup approximation property to arbitrary von Neumann algebras
AU - Caspers, Martijn
AU - Okayasu, Rui
AU - Skalski, Adam
AU - Tomatsu, Reiji
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2014/6
Y1 - 2014/6
N2 - 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.
AB - 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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U2 - 10.1016/j.crma.2014.04.003
DO - 10.1016/j.crma.2014.04.003
M3 - Article
AN - SCOPUS:84901637324
SN - 1631-073X
VL - 352
SP - 507
EP - 510
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 6
ER -