Quasinilpotent operators in operator Lie algebras II

Peng Cao¹

¹ Department of Mathematics Beijing Institute of Technology Beijing, China, 100081

Studia Mathematica, Tome 195 (2009) no. 2, pp. 193-200

Résumé

In this paper, it is proved that the Banach algebra $\overline{{\cal A}({\cal L})}$, generated by a Lie algebra $\cal L$ of operators, consists of quasinilpotent operators if $\cal L$ consists of quasinilpotent operators and $\overline{{\cal A}({\cal L})}$ consists of polynomially compact operators. It is also proved that $\overline{{\cal A}({\cal L})}$ consists of quasinilpotent operators if $\cal L$ 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.

Détail

DOI : 10.4064/sm195-2-6

Mots-clés : paper proved banach algebra overline cal cal generated lie algebra cal operators consists quasinilpotent operators cal consists quasinilpotent operators overline cal cal consists polynomially compact operators proved overline cal cal consists quasinilpotent operators cal essentially nilpotent engel lie algebra generated quasinilpotent operators finally banach algebras generated essentially nilpotent lie algebras shown compactly quasinilpotent