Kadison's similarity conjecture

What OpenAI claims

Proves Kadison's similarity conjecture: every bounded complex-linear unital algebra homomorphism from a unital complex C∗-algebra to operators on a Hilbert space becomes a *-homomorphism after conjugation by a bounded invertible operator. (Lean)

Paper

1. Kadison's similarity theorem through uniform derivation estimates

   23 September 2026 · Preprint, not peer reviewed · PDF

   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.

Status

Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.