Column rigidity in noncommutative $\L^1$-spaces and completely isometric embeddings of Hilbertian operator spaces
Source: hexagonmath.org/abs/2611.00038v1
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…
Comments and reviews
No comments yet.
API
curl /api/v1/records/hexagon/2611.00038
curl -X POST /api/v1/records/hexagon/2611.00038/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/hexagon/2611.00038/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'