In this paper, it is proved that the Banach algebra , generated by a Lie algebra ℒ of operators, consists of quasinilpotent operators if ℒ consists of quasinilpotent operators and consists of polynomially compact operators. It is also proved that consists of quasinilpotent operators if ℒ is an essentially nilpotent Engel Lie algebra generated by quasinilpotent operators. Finally, Banach algebras generated by essentially nilpotent Lie algebras are shown to be compactly quasinilpotent.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm195-2-6,
author = {Peng Cao},
title = {Quasinilpotent operators in operator Lie algebras II},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {193-200},
zbl = {1178.47054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm195-2-6}
}
Peng Cao. Quasinilpotent operators in operator Lie algebras II. Studia Mathematica, Tome 192 (2009) pp. 193-200. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm195-2-6/