Quasinilpotent operators in operator lie algebras II

Peng Cao

doi:10.4064/sm195-2-6

Quasinilpotent operators in operator lie algebras II

Peng Cao^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	193-200
Number of pages	8
Journal	Studia Mathematica
Volume	195
Issue number	2
DOIs	https://doi.org/10.4064/sm195-2-6
Publication status	Published - 2009

Keywords

Engel Lie algebras
Essentially nilpotent Lie algebras
Quasinilpotent operators

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Quasinilpotent operators in operator lie algebras II

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