LIE IDEALS IN TRIANGULAR OPERATOR-ALGEBRAS

Authors
HUDSON TD MARCOUX LW SOUROUR AR
Citation
Td. Hudson et al., LIE IDEALS IN TRIANGULAR OPERATOR-ALGEBRAS, Transactions of the American Mathematical Society, 350(8), 1998, pp. 3321-3339
Citations number
14
Categorie Soggetti
Mathematics,Mathematics
Journal title
Transactions of the American Mathematical Society → ACNP
ISSN journal
00029947
Volume
350
Issue
8
Year of publication
1998
Pages
3321 - 3339
Database
ISI
SICI code
0002-9947(1998)350:8<3321:LIITO>2.0.ZU;2-9
Abstract
We study Lie ideals in two classes of triangular operator algebras: ne st algebras and triangular UHF algebras. Our main results show that if L is a closed Lie ideal of the triangular operator algebra A, then th ere exist a closed associative ideal K and a closed subalgebra D-K of the diagonal A boolean AND A so that K subset of or equal to L subset of or equal to K + D-K.