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

• Datum: 2005
• Hauptverfasser: Rabanovych, V. I., Рабанович, В. І.
• Format: Artikel
• Sprache: Ukrainisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2005
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3606
• Назва журналу: 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...