An Elementary Proof of the Free-additivity of Voiculescu's Free Entropy

Details An Elementary Proof of the Free-additivity of Voiculescu's Free Entropy An Elementary Proof of the Free-additivity of Voiculescu's Free Entropy

2008-02-03

arxiv.org/abs/0802.0292v1

Mathematics

Operator Algebras

Scientific paper

D. Voiculescu [2] proved that a standard family of independent random unitary
k by k matrices and a constant k by k unitary matrix is asymtotically free as k
goes to infinity. This result was a key ingredient in Voiculescu's proof [3]
that his free entropy is additive when the variables are free. In this paper,
we give a very elementary proof of a more detailed version of this result [2].

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