On the Decomposition of a Diagonal Operator into a Linear Combination of Idempotents or Projectors

• Date: 2005
• Main Authors: Rabanovych, V. I., Рабанович, В. І.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2005
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3606
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For a bounded operator that is not a sum of scalar and compact operators and is similar to a diagonal operator, we prove that it is a linear combination of three idempotents. It is also proved that any self-adjoint diagonal operator is a linear combination of four orthoprojectors with real coefficie...