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Column rigidity in noncommutative $\L^1$-spaces and completely isometric embeddings of Hilbertian operator spaces

Source: hexagonmath.org/abs/2611.00038v1

Cédric ARHANCET

Hexagonhexagon/2611.00038Nov 3, 2026math.FAscore 0

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…

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