The case where the sum of three partial reflections is equal to zero

A.S. Mellit

Abstract

Up to unitary equivalence, we describe all irreducible triples of self-adjoint operators $A_1$, $A_2$, $A_3$ such that $\sigma(A_i)\subset \{−1, 0, 1\}$, $i = 1, 2, 3$, and $A_1 + A_2 + A_3 = 0$.