Lie algebras generated by Jordan operators

Peng Cao; Shanli Sun

doi:10.4064/sm186-3-5

Lie algebras generated by Jordan operators

Peng Cao^*, Shanli Sun

^*Corresponding author for this work

School of Mathematics and Statistics

Beihang University

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

Abstract

It is proved that if J_i is a Jordan operator on a Hilbert space with the Jordan decomposition J_i = N_i+Q_i, where N_i is normal and Q_i is compact and quasinilpotent, i = 1, 2, and the Lie algebra generated by J₁, J₂ is an Engel Lie algebra, then the Banach algebra generated by J₁, J₂ is an Engel algebra. Some results for normal operators and Jordan operators on Banach spaces are given.

Original language	English
Pages (from-to)	267-274
Number of pages	8
Journal	Studia Mathematica
Volume	186
Issue number	3
DOIs	https://doi.org/10.4064/sm186-3-5
Publication status	Published - 2008

Keywords

Engel Lie algebras
Jordan operators
Normal-equivalent operators

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10.4064/sm186-3-5

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AB - It is proved that if Ji is a Jordan operator on a Hilbert space with the Jordan decomposition Ji = Ni+Qi, where Ni is normal and Qi is compact and quasinilpotent, i = 1, 2, and the Lie algebra generated by J1, J2 is an Engel Lie algebra, then the Banach algebra generated by J1, J2 is an Engel algebra. Some results for normal operators and Jordan operators on Banach spaces are given.

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KW - Normal-equivalent operators

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Lie algebras generated by Jordan operators

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Keywords

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