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Quasinilpotent operators in operator Lie algebras II

Tom 195 / 2009

Peng Cao Studia Mathematica 195 (2009), 193-200 MSC: Primary 47B07; Secondary 47L70. DOI: 10.4064/sm195-2-6

Streszczenie

In this paper, it is proved that the Banach algebra $\overline{{\cal A}({\cal L})}$, generated by a Lie algebra $\cal L$ of operators, consists of quasinilpotent operators if $\cal L$ consists of quasinilpotent operators and $\overline{{\cal A}({\cal L})}$ consists of polynomially compact operators. It is also proved that $\overline{{\cal A}({\cal L})}$ consists of quasinilpotent operators if $\cal L$ 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.

Autorzy

  • Peng CaoDepartment of Mathematics
    Beijing Institute of Technology
    Beijing, China, 100081
    e-mail

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