Lie ideals in triangular operator algebras
Lie ideals in triangular operator algebras
We study Lie ideals in two classes of triangular operator algebras: nest algebras and triangular UHF algebras. Our main results show that if $\mathcal {L}$ is a closed Lie ideal of the triangular operator algebra $\mathbb {A}$, then there exist a closed associative ideal $\mathcal {K}$ and a closed subalgebra …