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 quasinilpotent 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 (fromto)  785798 
Number of pages  14 
Journal  Operators and Matrices 
Volume  8 
Issue number  3 
DOIs  
Publication status  Published  2014 
Keywords
 Elementary operator, quasinilpotent, locally linearly independent.
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Martin Mathieu
Person: Academic