### Abstract

Let A be a unital dense algebra of linear mappings on a complex vector
space X. Let φ =
Σ

^{n}_{i}=1 M_{ai},_{bi}be a locally quasi-nilpotent elementary operator of length n on A. We show that, if {a1, . . . , an} is locally linearly independent, then the local dimension of V (φ) = span{b_{i}a_{j}: 1 ≤ i, j ≤ n} is at most n(n−1) 2 . If ldim V (φ) = n(n−1) 2 , then there exists a representation of φ as φ = Σ^{n}_{i}=1 M_{ui},_{vi}with v_{i}u_{j}= 0 for i ≥ j. Moreover, we give a complete characterization of locally quasinilpotent elementary operators of length 3.Original language | English |
---|---|

Pages (from-to) | 785-798 |

Number of pages | 14 |

Journal | Operators and Matrices |

Volume | 8 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2014 |

### Keywords

- Elementary operator, quasi-nilpotent, locally linearly independent.

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## Cite this

Boudi, N., & Mathieu, M. (2014). Locally quasi-nilpotent elementary operators.

*Operators and Matrices*,*8*(3), 785-798. https://doi.org/10.7153/oam-08-44