Scalar Operators Representable as a Sum of Projectors
We study sets \(Σ _n = { α R^1 |\) there exist n projectors P1,...,Pn such that \(olimits_k = 1^n P_k = α I }\) . We prove that if n ≥ 6, then \({ 0,1,1 + 1n - 1 ,[ 1 + 1n - 2 ,n - 1 - 1n - 2 ],n - 1 - 1n - 1 ,n - 1,n } \) \(Σ _n { 0,1,1 + kk( n - 3 ) + 2 ,k N,[ 1 + 1n - 3 ,n - 1 - 1n - 3 ],n - 1 - kk( n - 3 ) + 2 ,k N,n - 1,n }\) ., number=7, journal=Ukrains’kyi Matematychnyi Zhurnal, author=Rabanovych, V. I. and Samoilenko, Yu. S., year=2001, month=Jul., pages=939–952