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Kadison’s similarity conjecture

Known results for nuclear algebras and other restricted classes do not establish the unrestricted bounded-representation target.

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Understand the problem ↓

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Understanding the problem

Read the background

Known results for nuclear algebras and other restricted classes do not establish the unrestricted bounded-representation target. The required similarity concerns one operator for the whole representation.

The theorem assumes a bounded unital complex-linear homomorphism. It is not a statement about arbitrary unbounded maps or an a priori uniform condition-number bound.

Why it matters

If correct, removes the stated restrictions from the bounded unital C*-algebra similarity target.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • The theorem assumes a bounded unital complex-linear homomorphism. It is not a statement about arbitrary unbounded maps or an a priori uniform condition-number bound.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

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