2010/01/19 by Lina Oliveira, Oliveira, Lina
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.OA #msc:17B60 #msc:47L35
paper · pdf · doi:10.48550/arxiv.1001.3269
17 pages; definitions missing in the previous version are now added at the beginning of Section 3 (page 3); results unchanged
arxiv created 2010/06/14 · arxiv updated 2010/06/15
The main theorem provides a characterisation of the finite rank operators lying in a norm closed Lie ideal of a continuous nest algebra. These operators are charaterised as those finite rank operators in the nest algebra satisfying a condition determined by a left order continuous homomorphism on the nest. A crucial fact used in the proof of this theorem is the decomposability of the finite rank operators. One shows that a finite rank operator in a norm closed Lie ideal of a continuous nest algebra can be written as a finite sum of rank one operators lying in the ideal.