OpenAI · 288-01 · 2026-09-23 · Operator algebras
Kadison's similarity theorem through uniform derivation estimates
preprints/Kadisons-similarity-theorem-through-uniform-derivation-estimates-September-23-2026
Family 288. Kadison's similarity conjecture.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Proves Kadison's similarity conjecture: every bounded complex-linear unital algebra homomorphism from a unital complex -algebra to operators on a Hilbert space becomes a -homomorphism after conjugation by a bounded invertible operator.
We prove that every bounded complex-linear unital algebra homomorphism from a unital complex C∗-algebra into the bounded operators on an arbitrary Hilbert space is similar to a -homomorphism. This resolves Kadison's similarity conjecture positively. We also obtain one universal hyperreflexivity constant for all unital von Neumann algebras on arbitrary complex Hilbert spaces.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 288: Kadison's similarity conjecture. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.