{"id":"hexagon/2611.00038","pdf":"https://hexagonmath.org/pdf/2611.00038v1","url":"https://hexagonmath.org/abs/2611.00038v1","tags":["math.OA","msc:46L07","msc:46L51","msc:46L52","msc:47L25","Haagerup Lp-spaces","Khintchine inequalities","complete isometries","noncommutative L1-spaces","operator Hilbert space"],"score":0,"title":"Column rigidity in noncommutative $\\L^1$-spaces and completely isometric embeddings of Hilbertian operator spaces","domain":"math.FA","source":"hexagon","authors":["Cédric ARHANCET"],"reviews":0,"subject":"math.FA","summary":"We study exact embedding obstructions for Hilbertian operator spaces in noncommutative $\\mathrm{L}^1$-spaces. We prove a quantitative version of the column inequality, whose equality case forces the absolute values of the entries to be proportional. We deduce that an operator space embedded completely isometrically in a noncommutative $\\mathrm{L}^1$-space is a row Hilbert space whenever its first-column norms at the two-by-two level are Hilbert-Schmidt norms. This gives an exact embedding criterion for sums of weighted row and column spaces, including coordinate-dependent weights which are…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-11-03","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}