Quintuplets of orthoprojectors associated by a linear relation

Abstract

We consider the equation $α_1 P_1 + α_2 P_2 + … α_n P_n = I$ over orthoprojectors $P_1, … ,P_n$ in a Hilbert space. We show that the set of real parameters $(α_1, … α_n)$ for which there exists a solution of this equation in orthoprojectors contains an open set from $ℝ^5$.