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

^*此作品的通讯作者

数学学院

Beihang University

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

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.

源语言	英语
页（从-至）	267-274
页数	8
期刊	Studia Mathematica
卷	186
期	3
DOI	https://doi.org/10.4064/sm186-3-5
出版状态	已出版 - 2008

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10.4064/sm186-3-5

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Cao, P., & Sun, S. (2008). Lie algebras generated by Jordan operators. Studia Mathematica, 186(3), 267-274. https://doi.org/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.

KW - Engel Lie algebras

KW - Jordan operators

KW - Normal-equivalent operators

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Lie algebras generated by Jordan operators

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