OpenAI research collection · 1 manuscript · Source checked 2026-10-19
OpenAI's result summary
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.
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MANUSCRIPT 01
Kadison's similarity theorem through uniform derivation estimates
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…
Full source abstract
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.
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New mathematical reasoning could help AI tackle harder scientific and computational problems. How reliably these skills transfer beyond mathematics will determine how much they contribute to general intelligence.