Quintuplets of orthoprojectors associated by a linear relation

• Date: 2009
• Main Authors: Yusenko, A. A., Юсенко, А. А.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2009
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3052
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 $ℝ^5$.