Israel Journal of Mathematics

, Volume 75, Issue 2–3, pp 273–275 | Cite as

A counter-example to a conjecture of Friedland

  • Takashi Yoshino


In 1982, S. Friedland proved that a bounded linear operator A on a Hilbert space is normal if and only if (αI + A + A*)2 ≧ AA* − A*A ≧ −(αI + A + A*)2 for all real α. And he conjectured the inequality (αI + A + A*)2 ≧ AA* − A*A for all real α will imply that A*A − AA* ≧ 0, i.e., A is hyponormal. But his conjecture is incorrect. In this note I’ll give a counter-example for his conjecture.


Hilbert Space Linear Operator Normal Operator Group Theory Orthonormal Basis 
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  1. 1.
    S. Friedland,A characterization of normal operators, Isr. J. Math.42 (1982), 235–240.MATHMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1991

Authors and Affiliations

  • Takashi Yoshino
    • 1
  1. 1.Department of Mathematics, College of General EducationTôhoku UniversitySendaiJapan

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