1Department of Mathematics Beijing Institute of Technology Beijing, China, 100081 2LMIB & Department of Mathematics Beihang University Beijing, China, 100083
Studia Mathematica, Tome 186 (2008) no. 3, pp. 267-274
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.
Keywords:
proved jordan operator hilbert space jordan decomposition i where normal compact quasinilpotent lie algebra generated engel lie algebra banach algebra generated engel algebra results normal operators jordan operators banach spaces given
Affiliations des auteurs :
Peng Cao
1
;
Shanli Sun
2
1
Department of Mathematics Beijing Institute of Technology Beijing, China, 100081
2
LMIB & Department of Mathematics Beihang University Beijing, China, 100083
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Peng Cao; Shanli Sun. Lie algebras generated by Jordan operators. Studia Mathematica, Tome 186 (2008) no. 3, pp. 267-274. doi: 10.4064/sm186-3-5
