Lie algebras generated by Jordan operators
Volume 186 / 2008
Studia Mathematica 186 (2008), 267-274
MSC: Primary 47B15; Secondary 47B47.
DOI: 10.4064/sm186-3-5
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 $J_1,J_2$ 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.
