The Case Where the Sum of Three Partial Reflections is Equal to Zero

Abstract

Up to unitary equivalence, we describe all irreducible triples of self-adjoint operators A ₁, A ₂, A ₃ such that σ(A _i) ⊂ |−1, 0, 1}, i = 1, 2, 3, and A ₁ + A ₂ + A ₃ = 0.