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 coefficie...
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| Date: | 2005 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2005
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3606 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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. |
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