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## Lie algebras generated by Jordan operators

### Tom 186 / 2008

Studia Mathematica 186 (2008), 267-274 MSC: Primary 47B15; Secondary 47B47. DOI: 10.4064/sm186-3-5

#### Streszczenie

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 $J_1,J_2$ is an Engel Lie algebra, then the Banach algebra generated by $J_1,J_2$ is an Engel algebra. Some results for normal operators and Jordan operators on Banach spaces are given.

#### Autorzy

• Peng CaoDepartment of Mathematics
Beijing Institute of Technology
Beijing, China, 100081
e-mail
• Shanli SunLMIB & Department of Mathematics
Beihang University
Beijing, China, 100083
e-mail

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