scholarly journals Positive-definite kernels, length functions on groups and a noncommutative von Neumann inequality

1989 ◽  
Vol 95 (2) ◽  
pp. 107-118 ◽  
Author(s):  
Marek Bożejko
Keyword(s):  
Positive Definite ◽  
Positive Definite Kernels ◽  
Length Functions ◽  
Von Neumann

scholarly journals Uniqueness of the von Neumann Continuous Factor

2018 ◽  
Vol 70 (5) ◽  
pp. 961-982 ◽  
Author(s):  
Pere Ara ◽  
Joan Claramunt
Keyword(s):  
Division Ring ◽  
Direct Limit ◽  
Positive Definite ◽  
Uniqueness Result ◽  
Rank Function ◽  
Von Neumann

AbstractFor a division ring D, denote by 𝓜D the D-ring obtained as the completion of the direct limit with respect to themetric induced by its unique rank function. We prove that, for any ultramatricial D-ring 𝓑 and any non-discrete extremal pseudo-rank function N on 𝓑, there is an isomorphism of D-rings , where stands for the completion of 𝓑 with respect to the pseudo-metric induced by N. This generalizes a result of von Neumann. We also show a corresponding uniqueness result for *-algebras over fields F with positive definite involution, where the algebra МF is endowed with its natural involution coming from the *-transpose involution on each of the factors .

scholarly journals THE ALPHA-BETA-SYMMETRIC DIVERGENCE AND THEIR POSITIVE DEFINITE KERNELS

2018 ◽  
Vol 53 (1) ◽  
pp. 75-100
Author(s):  
Mactar Ndaw ◽  
◽  
Macoumba Ndour ◽  
Papa Ngom ◽  
◽  
...  
Keyword(s):  
Positive Definite ◽  
Positive Definite Kernels ◽  
Alpha Beta
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