A hyperfinite inequality for free entropy dimension

Jung, Kenley

doi:10.1090/S0002-9939-06-08237-2

A hyperfinite inequality for free entropy dimension
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Proc. Amer. Math. Soc. 134 (2006), 2099-2108 Request permission

Abstract:

If $X, Y$, and $Z$ are finite sets of selfadjoint elements in a tracial von Neumann algebra and $X$ generates a hyperfinite von Neumann algebra, then $\delta _0(X \cup Y \cup Z) \leq \delta _0(X \cup Y) + \delta _0(X \cup Z)- \delta _0(X).$

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