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A hyperfinite inequality for free entropy dimension

Kenley Jung
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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 $δ_0(X \cup Y \cup Z) \leq δ_0(X \cup Y) + δ_0(X \cup Z) - δ_0(X).$ We draw several corollaries from this inequality.

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Kenley Jung. 2003-11-25. A hyperfinite inequality for free entropy dimension. https://arxiv.org/abs/math/0308271

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