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A hyperfinite inequality for free entropy dimension

Research paper by Kenley Jung

Indexed on: 25 Nov '03Published on: 25 Nov '03Published in: Mathematics - Operator Algebras



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 $\delta_0(X \cup Y \cup Z) \leq \delta_0(X \cup Y) + \delta_0(X \cup Z) - \delta_0(X).$ We draw several corollaries from this inequality.