Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 289-02. Near Inclusions of von Neumann Algebras Without Small Spatial Embeddings
Manuscript map · lines 8175–8184
OpenAI@2026-10-07#rem:oai-p-289-02
Authors: OpenAI. Family 289.
Title: Near Inclusions of von Neumann Algebras Without Small Spatial Embeddings.
Abstract: 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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