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Ukrainian Mathematical Journal

, Volume 56, Issue 3, pp 512–519 | Cite as

On the Decomposition of an Operator into a Sum of Four Idempotents

  • V. I. Rabanovych
Article

Abstract

We prove that operators of the form (2 ± 2/n)I + K are decomposable into a sum of four idempotents for integer n > 1 if there exists the decomposition K = K1K2 ⊕ ... ⊕ Kn, \(\sum\nolimits_1^n {K_i = 0} \), of a compact operator K. We show that the decomposition of the compact operator 4I + K or the operator K into a sum of four idempotents can exist if K is finite-dimensional. If n tr K is a sufficiently large (or sufficiently small) integer and K is finite-dimensional, then the operator (2 − 2/n)I + K [or (2 + 2/n)I + K] is a sum of four idempotents.

Keywords

Compact Operator 
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Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • V. I. Rabanovych
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKyiv

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