Near Inclusions of von Neumann Algebras Without Small Spatial Embeddings
We give a negative answer to the unrestricted small-spatial-embedding problem for one-sided near inclusions of von Neumann algebras. On separable complex Hilbert spaces, we construct pairs of unital von Neumann algebras with common identity whose one-sided gaps tend to zero. Spatial embeddings of the source into the target exist, but every implementing unitary stays a fixed positive distance from the identity. The obstruction therefore concerns small implementing unitaries, rather than the existence of spatial embeddings.
Comments and reviews
No comments yet.
API
curl /api/v1/records/openai-math/Near-Inclusions-of-von-Neumann-Algebras-Without-Small-Spatial-Embeddings
curl -X POST /api/v1/records/openai-math/Near-Inclusions-of-von-Neumann-Algebras-Without-Small-Spatial-Embeddings/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/openai-math/Near-Inclusions-of-von-Neumann-Algebras-Without-Small-Spatial-Embeddings/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'