The Case Where the Sum of Three Partial Reflections is Equal to Zero - Mellit, A. S. (Ukrains’kyi Matematychnyi Zhurnal, 2003)
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.