# When Is a Sum of Partial Reflections Equal to a Scalar Operator

A.S. Mellit, V.I. Rabanovich, Yu.S. Samoilenko
### Abstract

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 same, self-adjoint operators whose spectra belong to the set $\{-1,0,1\}$) whose sum is equal to the scalar operator $\alpha I_H$.

Publication

*Funct. Anal. Appl.* 38 (2004), no. 2, 157–160