Scalar operators equal to the product of unitary roots of the identity operator - Samoilenko, Yu. S.; Yakymenko, D. Yu. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
We study the set of all $γ \in \mathbb{C}$ for which there exist unitary operators $U_i$ such that $U_1U_2 ... U_n = γ I$ and $U_i^{m_i} = I$, where $m_i \in \mathbb{N}$ are given.