Universal Modules, Natural Pairings, and Weighted Isometries for Noncommutative $L^p$-Spaces
Source: hexagonmath.org/abs/2611.00114v1
For $1\le p 1$. For $1\le p,q 1$. A uniformly bounded natural inner product on every $L^p(M,\tau)$ exists exactly at $p=2$. For finite-dimensional unital embeddings preserving a faithful positive functional, we determine the nearest modularly compatible target density both in Hilbert--Schmidt norm and in the Hilbert--Schmidt distance between positive square roots. The minimum squared distance between square roots lies between a weighted sum of the losses in squared $L^2$ norm on matrix units and twice that sum. Both constants are sharp.
Comments and reviews
No comments yet.
API
curl /api/v1/records/hexagon/2611.00114
curl -X POST /api/v1/records/hexagon/2611.00114/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/hexagon/2611.00114/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'