Abstract
We describe the set \(\widetilde W_n\) of values of the parameter α∈ℝ for which there exists a Hilbert space H and n partial reflections A 1,...,A n (self-adjoint operators such that A 3k =Ak 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 α I H .
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Mellit, A.S., Rabanovich, V.I. & Samoilenko, Y.S. When Is a Sum of Partial Reflections Equal to a Scalar Operator?. Functional Analysis and Its Applications 38, 157–160 (2004). https://doi.org/10.1023/B:FAIA.0000034047.27498.51
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DOI: https://doi.org/10.1023/B:FAIA.0000034047.27498.51