摘要
In this paper, it is proved that the Banach algebra A(ℒ)macr;, generated by a Lie algebra ℒ of operators, consists of quasinilpotent operators if ℒ consists of quasinilpotent operators and A(ℒ)̄ consists of polynomially compact operators. It is also proved that A(ℒ)̄ 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.
| 源语言 | 英语 |
|---|---|
| 页（从-至） | 193-200 |
| 页数 | 8 |
| 期刊 | Studia Mathematica |
| 卷 | 195 |
| 期 | 2 |
| DOI | |
| 出版状态 | 已出版 - 2009 |