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

Authors

  • V. I. Rabanovych

Abstract

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 coefficients.

Published

25.03.2005

Issue

Section

Research articles

How to Cite

Rabanovych, V. I. “On the Decomposition of a Diagonal Operator into a Linear Combination of Idempotents or Projectors”. Ukrains’kyi Matematychnyi Zhurnal, vol. 57, no. 3, Mar. 2005, pp. 388–393, https://umj.imath.kiev.ua/index.php/umj/article/view/3606.