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A proof of the spectral isometry conjecture for C*-algebras

Matthew J. Colbrook, George Stepaniants

Palomar Registrypalomar/PALOMAR-2026-10-28-000031Oct 28, 2026math.OAscore 0

A formal proof that every unital surjective complex-linear spectral isometry between arbitrary complex unital C*-algebras is an algebraic Jordan isomorphism. The development also proves that a bounded generator whose exponentials are unital spectral isometries at every complex parameter is an associative derivation, and that every surjective spectral isometry is a unital Jordan isomorphism multiplied by its prescribed central unitary value at the identity.

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