On quadruples of projectors connected by a linear relation

Abstract

We describe the set of γ ∈ ℝ for which there exist quadruples of projectors P i for a fixed collection of numbers $\alpha_i \in \mathbb{R}_+, \quad i = \overline{1,4}$, такі, що $\alpha_1 P_1 + \alpha_2 P_2 + \alpha_3 P_3 + \alpha_4 P_4 = \gamma I$