### Abstract

Let 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 A is 2-transitive, then it is dense, and (2) if A is n-transitive, n ≥ 1, then a nonzero Jordan ideal of A is also n-transitive. These answer two questions posed by Grünenfelder, Omladič and Radjavi.

Original language | English |
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Pages (from-to) | 579-584 |

Number of pages | 6 |

Journal | Integral Equations and Operator Theory |

Volume | 62 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2008 Dec 1 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Algebra and Number Theory

### Cite this

*Integral Equations and Operator Theory*,

*62*(4), 579-584. https://doi.org/10.1007/s00020-008-1608-3

}

*Integral Equations and Operator Theory*, vol. 62, no. 4, pp. 579-584. https://doi.org/10.1007/s00020-008-1608-3

**Transitivity of Jordan algebras of linear operators : On two questions by Grünenfelder, Omladič and Radjavi.** / Chebotar, Mikhail; Ke, Wen-Fong; Lomonosov, Victor.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Transitivity of Jordan algebras of linear operators

T2 - On two questions by Grünenfelder, Omladič and Radjavi

AU - Chebotar, Mikhail

AU - Ke, Wen-Fong

AU - Lomonosov, Victor

PY - 2008/12/1

Y1 - 2008/12/1

N2 - Let 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 A is 2-transitive, then it is dense, and (2) if A is n-transitive, n ≥ 1, then a nonzero Jordan ideal of A is also n-transitive. These answer two questions posed by Grünenfelder, Omladič and Radjavi.

AB - Let 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 A is 2-transitive, then it is dense, and (2) if A is n-transitive, n ≥ 1, then a nonzero Jordan ideal of A is also n-transitive. These answer two questions posed by Grünenfelder, Omladič and Radjavi.

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UR - http://www.scopus.com/inward/citedby.url?scp=58149125753&partnerID=8YFLogxK

U2 - 10.1007/s00020-008-1608-3

DO - 10.1007/s00020-008-1608-3

M3 - Article

VL - 62

SP - 579

EP - 584

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 4

ER -