Mathematics – Operator Algebras
Scientific paper
2010-01-19
Mathematics
Operator Algebras
17 pages; definitions missing in the previous version are now added at the beginning of Section 3 (page 3); results unchanged
Scientific paper
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.
Oliveira Lina
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