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.
released 2026-09-23 | 4 theorems · 15 lemmas · 23 proofs · 12,800 words |
PLAY LEVEL 1 »(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.