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Kadison's similarity conjecture
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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Kadison's similarity theorem through uniform derivation estimates
Sep 23, 2026·paper.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.