Scalar Operators Representable as a Sum of Projectors

• Datum: 2001
• Hauptverfasser: Rabanovych, V. I., Samoilenko, Yu. S., Рабанович, В. И., Самойленко, Ю. С.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2001
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/4315
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We study sets \(\Sigma _n = \{ \alpha \in \mathbb{R}^1 |\) there exist n projectors P1,...,Pn such that \(\sum\nolimits_{k = 1}^n {P_k = \alpha I} \}\) . We prove that if n ≥ 6, then \(\left\{ {0,1,1 + \frac{1}{{n - 1}},\left[ {1 + \frac{1}{{n - 2}},n - 1 - \frac{1}{{n - 2}}} \right],n - 1...