A hyperfinite inequality for free entropy dimension

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 ${\delta }_0(X\cup Y\cup Z)\le {\delta }_0(X\cup Y)+{\delta }_0(X\cup Z)-{\delta }_0(X).$ We draw several corollaries from this inequality.

9 pages, added section and corollary