Integral Equations and Operator Theory

, Volume 62, Issue 4, pp 579–584 | Cite as

Transitivity of Jordan Algebras of Linear Operators: On Two Questions by Grünenfelder, Omladič and Radjavi

  • Mikhail ChebotarEmail author
  • Wen-Fong Ke
  • Victor Lomonosov


Let \({{\mathcal{A}}}\) be a Jordan algebra of linear operators on a vector space over a field of characteristic different from 2. In this short note, we show that (1) if \({\mathcal{A}}\) is 2-transitive, then it is dense, and (2) if \({\mathcal{A}}\) is n-transitive, n ≥ 1, then a nonzero Jordan ideal of \({{\mathcal{A}}}\) is also n-transitive. These answer two questions posed by Grünenfelder, Omladič and Radjavi.

Mathematics Subject Classification (2000).

Primary 47A15 Secondary 17C50 


Jordan algebra n-transitivity 


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Copyright information

© Birkhaueser 2008

Authors and Affiliations

  • Mikhail Chebotar
    • 1
    Email author
  • Wen-Fong Ke
    • 2
  • Victor Lomonosov
    • 1
  1. 1.Department of Mathematical SciencesKent State UniversityKentUSA
  2. 2.Department of MathematicsNational Cheng Kung University and National Center for Theoretical Sciences (South)TainanTaiwan

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