scholarly journals Absence of algebraic relations and of zero divisors under the assumption of full non-microstates free entropy dimension

2017 ◽  
Vol 304 ◽  
pp. 1080-1107 ◽  
Author(s):  
Tobias Mai ◽  
Roland Speicher ◽  
Moritz Weber
Keyword(s):  
Free Entropy ◽  
Entropy Dimension ◽  
Zero Divisors ◽  
Free Entropy Dimension

scholarly journals Free entropy dimension and regularity of non-commutative polynomials

2016 ◽  
Vol 271 (8) ◽  
pp. 2274-2292 ◽  
Author(s):  
Ian Charlesworth ◽  
Dimitri Shlyakhtenko
Keyword(s):  
Free Entropy ◽  
Entropy Dimension ◽  
Free Entropy Dimension

FREE ENTROPY DIMENSION OF PROJECTIONS AND FACTORIALITY OF GENERATED VON NEUMANN ALGEBRAS

2008 ◽  
Vol 11 (02) ◽  
pp. 295-305
Author(s):  
TAKUHO MIYAMOTO
Keyword(s):  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Sufficient Condition ◽  
Von Neumann ◽  
Free Entropy ◽  
Entropy Dimension ◽  
Free Entropy Dimension

We examine the free entropy and free entropy dimension for projections, and obtain a sufficient condition for the factoriality of the von Neumann algebra generated by projections in terms of their free entropy dimension. This corresponds to Voiculescu's result for self-adjoint elements.

scholarly journals ORBITAL APPROACH TO MICROSTATE FREE ENTROPY

2009 ◽  
Vol 20 (02) ◽  
pp. 227-273 ◽  
Author(s):  
FUMIO HIAI ◽  
TAKUHO MIYAMOTO ◽  
YOSHIMICHI UEDA
Keyword(s):  
Random Variables ◽  
Free Entropy ◽  
Basic Properties ◽  
Entropy Dimension ◽  
Orbital Free ◽  
Free Entropy Dimension

Motivated by Voiculescu's liberation theory, we introduce the orbital free entropy χ orb for non-commutative self-adjoint random variables (also for "hyperfinite random multi-variables"). Besides its basic properties, the relation of χorb with the usual free entropy χ is shown. Moreover, the dimension counterpart δ0, orb of χ orb is discussed, and we obtain the relation between δ0, orb and the original free entropy dimension δ0 together with applications to δ0 itself.

scholarly journals MF-traces and a lower bound for the topological free entropy dimension in unital C*-algebras

2014 ◽  
Vol 71 (1) ◽  
pp. 15-44 ◽  
Author(s):  
Qihui Li ◽  
Don Hadwin ◽  
Weihua Li ◽  
Junhao Shen
Keyword(s):  
Lower Bound ◽  
Free Entropy ◽  
C Algebras ◽  
Entropy Dimension ◽  
Free Entropy Dimension
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