The Commutation Theorem for Tensor Products of von Neumann Algebras

1975 ◽  
Vol 7 (3) ◽  
pp. 257-260 ◽  
Author(s):  
Marc A. Rieffel ◽  
Alfons van Daele
Keyword(s):  
Von Neumann Algebras ◽  
Tensor Products ◽  
Von Neumann

Extension of normal functionals on W*-tensor products

1975 ◽  
Vol 78 (2) ◽  
pp. 301-307 ◽  
Author(s):  
Simon Wassermann
Keyword(s):  
Representation Theory ◽  
Tensor Product ◽  
Hilbert Spaces ◽  
General Result ◽  
Von Neumann Algebras ◽  
Tensor Products ◽  
Von Neumann ◽  
Hilbert Algebras ◽  
Special Cases

A deep result in the theory of W*-tensor products, the Commutation theorem, states that if M and N are W*-algebras faithfully represented as von Neumann algebras on the Hilbert spaces H and K, respectively, then the commutant in L(H ⊗ K) of the W*-tensor product of M and N coincides with the W*-tensor product of M′ and N′. Although special cases of this theorem were established successively by Misonou (2) and Sakai (3), the validity of the general result remained conjectural until the advent of the Tomita-Takesaki theory of Modular Hilbert algebras (6). As formulated, the Commutation theorem is a spatial result; that is, the W*-algebras in its statement are taken to act on specific Hilbert spaces. Not surprisingly, therefore, known proofs rely heavily on techniques of representation theory.

On tensor products of von Neumann algebras

1996 ◽  
Vol 123 (1) ◽  
pp. 453-466 ◽  
Author(s):  
L. Ge ◽  
R. Kadison
Keyword(s):  
Von Neumann Algebras ◽  
Tensor Products ◽  
Von Neumann

STRANGE PROJECTIONS IN TENSOR PRODUCTS OF VON NEUMANN ALGEBRAS

1995 ◽  
Vol 46 (2) ◽  
pp. 197-199 ◽  
Author(s):  
KAZUYUKI SAITÔ ◽  
J. D. MAITLAND WRIGHT
Keyword(s):  
Von Neumann Algebras ◽  
Tensor Products ◽  
Von Neumann

scholarly journals Groupoid normalisers of tensor products: infinite von Neumann algebras

2013 ◽  
Vol 69 (2) ◽  
pp. 545-570 ◽  
Author(s):  
Junsheng Fang ◽  
Roger R. Smith ◽  
Stuart White
Keyword(s):  
Von Neumann Algebras ◽  
Tensor Products ◽  
Von Neumann

scholarly journals On the commutation theorem for tensor products of von Neumann algebras

1976 ◽  
Vol 61 (1) ◽  
pp. 179-179
Author(s):  
R. Rousseau ◽  
Alfons van Daele ◽  
L. Vanheeswijck
Keyword(s):  
Von Neumann Algebras ◽  
Tensor Products ◽  
Von Neumann

scholarly journals Some prime factorization results for free quantum group factors

2017 ◽  
Vol 2017 (722) ◽  
Author(s):  
Yusuke Isono
Keyword(s):  
Quantum Group ◽  
Von Neumann Algebras ◽  
Tensor Products ◽  
Crossed Product ◽  
Direct Products ◽  
Unique Factorization ◽  
Prime Factorization ◽  
Von Neumann ◽  
Type Iii ◽  
Original Type

AbstractWe prove some unique factorization results for tensor products of free quantum group factors. They are type III analogues of factorization results for direct products of bi-exact groups established by Ozawa and Popa. In the proof, we first take continuous cores of the tensor products, which satisfy a condition similar to condition (AO), and discuss some factorization properties for the continuous cores. We then deduce factorization properties for the original type III factors. We also prove some unique factorization results for crossed product von Neumann algebras by direct products of bi-exact groups.

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 :

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