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 |
指纹
探究 'Quasinilpotent operators in operator lie algebras II' 的科研主题。它们共同构成独一无二的指纹。引用此
Cao, P. (2009). Quasinilpotent operators in operator lie algebras II. Studia Mathematica, 195(2), 193-200. https://doi.org/10.4064/sm195-2-6