On products of symmetries in von Neumann algebras

B V Rajarama Bhat, Soumyashant Nayak, P Shankar

Let $\mathcal{R}$ be a type $I{I}_1$ von Neumann algebra. We show that every unitary in $\mathcal{R}$ may be decomposed as the product of six symmetries (that is, self-adjoint unitar…