scholarly journals Haagerup Approximation Property for Arbitrary von Neumann Algebras

2015 ◽  
Vol 51 (3) ◽  
pp. 567-603 ◽  
Author(s):  
Rui Okayasu ◽  
Reiji Tomatsu
Keyword(s):  
Approximation Property ◽  
Von Neumann Algebras ◽  
Von Neumann

scholarly journals Generalisations of the Haagerup approximation property to arbitrary von Neumann algebras

2014 ◽  
Vol 352 (6) ◽  
pp. 507-510 ◽  
Author(s):  
Martijn Caspers ◽  
Rui Okayasu ◽  
Adam Skalski ◽  
Reiji Tomatsu
Keyword(s):  
Approximation Property ◽  
Von Neumann Algebras ◽  
Von Neumann

The Haagerup invariant for tensor products of operator spaces

1996 ◽  
Vol 120 (1) ◽  
pp. 147-153 ◽  
Author(s):  
Allan M. Sinclair ◽  
Roger R. Smith
Keyword(s):  
Tensor Product ◽  
Approximation Property ◽  
Von Neumann Algebras ◽  
Tensor Products ◽  
Dual Operator ◽  
Operator Spaces ◽  
Von Neumann

In [7, 8] Haagerup introduced two isomorphism invariants and for C*-algebras and von Neumann algebras , based on appropriate forms of the completely bounded approximation property defined below. These definitions have obvious extensions to operator spaces and dual operator spaces respectively, and in [16] we established the multiplicativity of A on the ultraweakly closed spatial tensor product of two dual operator spaces and :

scholarly journals Haagerup approximation property via bimodules

2017 ◽  
Vol 121 (1) ◽  
pp. 75 ◽  
Author(s):  
Rui Okayasu ◽  
Narutaka Ozawa ◽  
Reiji Tomatsu
Keyword(s):  
Quantum Group ◽  
Von Neumann Algebra ◽  
Approximation Property ◽  
Von Neumann Algebras ◽  
Locally Compact ◽  
Haagerup Property ◽  
Von Neumann ◽  
Locally Compact Quantum Groups ◽  
Locally Compact Quantum Group ◽  
Finite Von Neumann Algebras

The Haagerup approximation property (HAP) is defined for finite von Neumann algebras in such a way that the group von Neumann algebra of a discrete group has the HAP if and only if the group itself has the Haagerup property. The HAP has been studied extensively for finite von Neumann algebras and it was recently generalized to arbitrary von Neumann algebras by Caspers-Skalski and Okayasu-Tomatsu. One of the motivations behind the generalization is the fact that quantum group von Neumann algebras are often infinite even though the Haagerup property has been defined successfully for locally compact quantum groups by Daws-Fima-Skalski-White. In this paper, we fill this gap by proving that the von Neumann algebra of a locally compact quantum group with the Haagerup property has the HAP. This is new even for genuine locally compact groups.

Correspondences and Approximation Properties for von Neumann Algebras

2003 ◽  
Vol 14 (06) ◽  
pp. 619-665 ◽  
Author(s):  
Jon Kraus
Keyword(s):  
Approximation Property ◽  
Von Neumann Algebras ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Approximation Properties ◽  
Locally Compact ◽  
Von Neumann ◽  
Weak Amenability ◽  
Operator Approximation ◽  
Weak Operator

The notion of the amenability of a locally compact group has been extended in various ways. Two weaker versions of amenability, weak amenability and the approximation property, have been defined for locally compact groups (by Haagerup and Haagerup and Kraus, respectively) and Bekka has defined a notion of amenability for representations of locally compact groups. Correspondences can be viewed as a generalization of representations of such groups. Using this viewpoint, Ananthraman–Delaroche has defined a notion of (left) amenability for correspondences. In this paper, we define notions of weak amenability and the approximation property for correspondences (and representations of locally compact groups), and obtain various results concerning these notions. Ananthraman–Delaroche showed that if N ⊂ M is an inclusion of von Neumann algebras, and if the associated inclusion correspondence is left amenable, then various approximation properties of N (semidiscreteness, the weak* completely bounded approximation property, and the weak* operator approximation property) are shared by M. We show that if this correspondence has the (weaker) approximation property, then if N has the weak* operator approximation property, so does M. An application of this result to crossed products is also given.

Lectures on von Neumann Algebras

2019 ◽  
Author(s):  
Serban-Valentin Stratila ◽  
Laszlo Zsido
Keyword(s):  
Von Neumann Algebras ◽  
Von Neumann
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