On the Decomposition of a Diagonal Operator into a Linear Combination of Idempotents or Projectors
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.
English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 3, pp 466-473.
Citation Example: Rabanovych V. I. On the Decomposition of a Diagonal Operator into a Linear Combination of Idempotents or Projectors // Ukr. Mat. Zh. - 2005. - 57, № 3. - pp. 388–393.