Abstract
It is proved that the nilpotent Lie algebra generated by a family of decomposable operators generates an Engel- Banach algebra. We also proved that if a Lie algebra of quasinilpotent operators is essentially nilpotent, then the Banach algebra generated by this Lie algebra consists of quasinilpotent operators.
| Original language | English |
|---|---|
| Pages (from-to) | 35-41 |
| Number of pages | 7 |
| Journal | Integral Equations and Operator Theory |
| Volume | 58 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - May 2007 |
| Externally published | Yes |
Keywords
- Decomposable operator
- Engel Lie algebra
- Quasinilpotent operator