2017
Том 69
№ 9

All Issues

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

Rabanovych V. I.

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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.

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.

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