Subadditivity Inequalities in von Neumann Algebras and Characterization of Tracial Functionals

Positivity ◽  
2005 ◽  
Vol 9 (2) ◽  
pp. 259-264 ◽  
Author(s):  
O. E. Tikhonov
Keyword(s):  
Von Neumann Algebras ◽  
Von Neumann

scholarly journals Characterization of Lie derivations on von Neumann algebras

2013 ◽  
Vol 438 (1) ◽  
pp. 533-548 ◽  
Author(s):  
Xiaofei Qi ◽  
Jinchuan Hou
Keyword(s):  
Von Neumann Algebras ◽  
Von Neumann ◽  
Lie Derivations

scholarly journals Dual Banach algebras: Connes-amenability, normal, virtual diagonals, and injectivity of the predual bimodule

2004 ◽  
Vol 95 (1) ◽  
pp. 124 ◽  
Author(s):  
Volker Runde
Keyword(s):  
Abelian Subgroup ◽  
Von Neumann Algebras ◽  
Banach Algebras ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Von Neumann ◽  
Connes Amenability ◽  
Definition Of ◽  
Dual Banach Algebra

Let $\mathcal A$ be a dual Banach algebra with predual $\mathcal A_*$ and consider the following assertions: (A) $\mathcal A$ is Connes-amenable; (B) $\mathcal A$ has a normal, virtual diagonal; (C) $\mathcal A_*$ is an injective $\mathcal A$-bimodule. For general $\mathcal A$, all that is known is that (B) implies (A) whereas, for von Neumann algebras, (A), (B), and (C) are equivalent. We show that (C) always implies (B) whereas the converse is false for $\mathcal A = M(G)$ where $G$ is an infinite, locally compact group. Furthermore, we present partial solutions towards a characterization of (A) and (B) for $\mathcal A = B(G)$ in terms of $G$: For amenable, discrete $G$ as well as for certain compact $G$, they are equivalent to $G$ having an abelian subgroup of finite index. The question of whether or not (A) and (B) are always equivalent remains open. However, we introduce a modified definition of a normal, virtual diagonal and, using this modified definition, characterize the Connes-amenable, dual Banach algebras through the existence of an appropriate notion of virtual diagonal.

A characterization of von Neumann algebras

2010 ◽  
Vol 76 (3-4) ◽  
pp. 561-580
Author(s):  
János Kristóf
Keyword(s):  
Von Neumann Algebras ◽  
Von Neumann
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