2003/12/11 by Kenley Jung, Jung, Kenley
Computer Science · Mathematics · #28A78 #46L54 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Operator Algebras (math.OA) #Topological and Geometric Data Analysis #math.OA #msc:28A78 #msc:46L54
paper · pdf · doi:10.48550/arxiv.math/0312223
9 pages
arxiv created 2003/12/11 · openalex publication_date 2003/12/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a selfadjoint element x in a tracial von Neumann algebra and α= δ0(x) we compute bounds for \mathbb Hα(x), where \mathbb Hα(x) is the free Hausdorff α-entropy of x. The bounds are in terms of ∫ ∫\mathbb R2 -D log |y-z| dμ(y) dμ(z) where μ is the Borel measure on the spectrum of x induced by the trace and D ⊂ \mathbb R2 is the diagonal. We compute similar bounds for the free Hausdorff entropy of a free family of selfadjoints.