On the Decomposition of an Operator into a Sum of Four Idempotents

• Date: 2004
• Main Authors: Rabanovych, V. I., Рабанович, В. І.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2004
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3764
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We prove that operators of the form (2 ± 2/n)I + K are decomposable into a sum of four idempotents for integer n > 1 if there exists the decomposition K = K 1 ⊕ K 2 ⊕ ... ⊕ K n, \(\sum\nolimits_1^n {K_i = 0} \) , of a compact operator K. We show that the decomposition of the compact operat...