Graphs of functions and vanishing free entropy

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dc.creatorJung, Kenley
dc.date2007-07-10
dc.date.accessioned2026-07-07T08:14:48Z
dc.date.available2026-07-07T08:14:48Z
dc.descriptionSuppose X is an n-tuple of selfadjoint elements in a tracial von Neumann algebra M. If z is a selfadjoint element in M and for some selfadjoint element y in the von Neumann algebra generated by X $δ_0(y, z) < δ_0(y) + δ_0(z)$, then $χ(X \cup \{z\}) = -\infty$ (here $χ$ and $δ_0$ denote the microstates free entropy and free entropy dimension, respectively). In particular, if z lies in the von Neumann algebra generated by X, then $χ(X \cup \{z\}) = -\infty$. The statement and its proof are motivated by geometric-measure-theoretic results on graphs of functions. A similar statement for the nonmicrostates free entropy is obtained under the much stronger hypothesis that z lies in the algebra generated by X.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/0707.1355
dc.identifierhttp://arxiv.org/abs/0707.1355
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/133259
dc.subjectOperator Algebras
dc.subject46L54 (Primary), 28A75 (Secondary)
dc.titleGraphs of functions and vanishing free entropy
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