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Quasinilpotent Operators in Operator Lie Algebras

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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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Authors and Affiliations

  1. LMIB & Department of Mathematics, Beihang University, Beijing, 100083, China

    Peng Cao & Shanli Sun

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  1. Peng Cao
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  2. Shanli Sun
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Correspondence to Peng Cao.

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Cao, P., Sun, S. Quasinilpotent Operators in Operator Lie Algebras. Integr. equ. oper. theory 58, 35–41 (2007). https://doi.org/10.1007/s00020-006-1474-9

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  • DOI: https://doi.org/10.1007/s00020-006-1474-9

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