Locally quasi-nilpotent elementary operators

Nadia Boudi, Martin Mathieu

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Abstract

Let A be a unital dense algebra of linear mappings on a complex vector space X. Let φ = Σn i=1 Mai,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{biaj : 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 = Σn i=1 Mui,vi with viuj = 0 for i ≥ j. Moreover, we give a complete characterization of locally quasinilpotent elementary operators of length 3.
Original languageEnglish
Pages (from-to)785-798
Number of pages14
JournalOperators and Matrices
Volume8
Issue number3
DOIs
Publication statusPublished - 2014

Keywords

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

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