scholarly journals Lower estimates on microstates free entropy dimension

2009 ◽  
Vol 2 (2) ◽  
pp. 119-146 ◽  
Author(s):  
Dimitri Shlyakhtenko
Keyword(s):  
Free Entropy ◽  
Entropy Dimension ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document