We describe the set $\tilde{\mathcal{W}\_n}$ of values of the parameter $\alpha\in\mathbb{R}$ for which there exists a Hilbert space $H$ and $n$ partial reflections $A\_1,\ldots,A\_n$ (self-adjoint operators such that $A\_k^3 =A\_k$ or, which is the …
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 $A\_1 + A\_2 + A\_3 = 0$.