On Jones' Criterion for Optimum Lifting Wings

1958 ◽  
Vol 25 (9) ◽  
pp. 600-600 ◽  
Author(s):  
Hideo Yoshihara ◽  
Torstsin Strand
Keyword(s):  
Jones Criterion

scholarly journals Fullness of crossed products of factors by discrete groups

2019 ◽  
Vol 150 (5) ◽  
pp. 2368-2378 ◽  
Author(s):  
Amine Marrakchi
Keyword(s):  
Discrete Group ◽  
Amenable Group ◽  
Complete Characterization ◽  
Crossed Product ◽  
Discrete Groups ◽  
Sufficient Condition ◽  
Crossed Products ◽  
Product Factor ◽  
Jones Criterion ◽  
Arbitrary Factor

AbstractLet M be an arbitrary factor and $\sigma : \Gamma \curvearrowright M$ an action of a discrete group. In this paper, we study the fullness of the crossed product $M \rtimes _\sigma \Gamma $. When Γ is amenable, we obtain a complete characterization: the crossed product factor $M \rtimes _\sigma \Gamma $ is full if and only if M is full and the quotient map $\overline {\sigma } : \Gamma \rightarrow {\rm out}(M)$ has finite kernel and discrete image. This answers the question of Jones from [11]. When M is full and Γ is arbitrary, we give a sufficient condition for $M \rtimes _\sigma \Gamma $ to be full which generalizes both Jones' criterion and Choda's criterion. In particular, we show that if M is any full factor (possibly of type III) and Γ is a non-inner amenable group, then the crossed product $M \rtimes _\sigma \Gamma $ is full.

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