LOCALLY QUASI-NILPOTENT ELEMENTARY OPERATORS

作者：Boudi Nadia^*; Mathieu Martin

来源：Operators and Matrices, 2014, 8(3): 785-798.

DOI：10.7153/oam-08-44

• Elementary operator
• quasi-nilpotent
• locally linearly independent

Let A be a unital dense algebra of linear mappings on a complex vector space X. Let phi = Sigma(n)(i=1) M-ai,M-bi be a locally quasi-nilpotent elementary operator of length n on A. We show that, if {a(1), ..., a(n)} is locally linearly independent, then the local dimension of V(phi) = span{b(i)a(j) : 1 %26lt;= i, j %26lt;= n} is at most n(n-1)/2. If ldimV(phi) = n(n-1)/2, then there exists a representation of phi as phi = Sigma(n)(i=1) M-ui,M-vi with v(i)u(j) = 0 for i %26gt;= j. Moreover, we give a complete characterization of locally quasi-nilpotent elementary operators of length 3.

• 出版日期2014-9