{"id":"hexagon/2610.00555","pdf":"https://hexagonmath.org/pdf/2610.00555v1","url":"https://hexagonmath.org/abs/2610.00555v1","tags":["math.OA","msc:46L07","msc:46L51","msc:46L52","msc:46L54","msc:47L25","circular elements","complete isometries","noncommutative $\\L^1$-spaces","operator Hilbert space"],"score":0,"title":"The operator Hilbert space $\\mathrm{OH}$ embeds completely isometrically into a noncommutative $\\mathrm{L}^1$-space","domain":"math.FA","source":"hexagon","authors":["Cédric ARHANCET"],"reviews":0,"subject":"math.FA","summary":"We prove that Pisier's operator Hilbert space $\\mathrm{OH}$ embeds completely isometrically into the predual of a $\\mathrm{QWEP}$ von Neumann algebra, answering a longstanding question introduced by Pisier and later by Haagerup and Musat. The embedding is obtained as an ultraproduct of free probabilistic models $h_k = \\Lambda^{\\frac{1}{2}}c_k\\Lambda^{\\frac{1}{2}}$ realized in the free group factor $\\mathrm{VN}(\\mathbb{F}_\\infty)$, with the trace and circular family scaled according to the mass of the truncated measure $t^{-\\frac{5}{3}} \\mathrm{d} t$.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-26","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}