Scalar Operators Representable as a Sum of Projectors

  • V. I. Rabanovych
  • Yu. S. Samoilenko Iн-т математики НАН України, Київ

Abstract

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 \(\left\{ {0,1,1 + \frac{1}{{n - 1}},\left[ {1 + \frac{1}{{n - 2}},n - 1 - \frac{1}{{n - 2}}} \right],n - 1 - \frac{1}{{n - 1}},n - 1,n} \right\} \supset\) \(\Sigma _n \supset \left\{ {0,1,1 + \frac{k}{{k\left( {n - 3} \right) + 2}},k \in \mathbb{N},\left[ {1 + \frac{1}{{n - 3}},n - 1 - \frac{1}{{n - 3}}} \right],n - 1 - \frac{k}{{k\left( {n - 3} \right) + 2}},k \in \mathbb{N},n - 1,n} \right\}\) .
Published
25.07.2001
How to Cite
RabanovychV. I., and SamoilenkoY. S. “Scalar Operators Representable As a Sum of Projectors”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 53, no. 7, July 2001, pp. 939-52, https://umj.imath.kiev.ua/index.php/umj/article/view/4315.
Section
Research articles