Decomposition of a unitary scalar operator into a product of roots of the identity - Yakymenko, D. Yu. (Methods of Functional Analysis and Topology, 2013)
We prove that for all m_1,m_2,m_3 N, 1m_1+1m_2+1m_3 ≤ 1, every unitary scalar operator γ I on a complex infinite-dimensional Hilbert space is a product γ I = U_1 U_2 U_3 where U_i is a unitary operator such that U_i^m_i = I.