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Israel Journal of Mathematics

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

A counter-example to a conjecture of Friedland

  • Takashi Yoshino
Article
  • 41 Downloads

Abstract

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.

Keywords

Hilbert Space Linear Operator Normal Operator Group Theory Orthonormal Basis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  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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