Quasinilpotent Operators in Operator Lie Algebras |
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Authors: | Peng Cao Shanli Sun |
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Affiliation: | (1) LMIB & Department of Mathematics, Beihang University, Beijing, 100083, China |
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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. |
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Keywords: | Primary 47B48 Secondary 47L70 |
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