Lie algebras generated by Jordan operators

Peng Cao; Shanli Sun

Peng Cao ; Shanli Sun

Studia Mathematica, Tome 187 (2008), p. 267-274 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Publié le : 2008-01-01

Zbl 1167.47055

EUDML-ID : urn:eudml:doc:284512

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     title = {Lie algebras generated by Jordan operators},
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     volume = {187},
     year = {2008},
     pages = {267-274},
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     language = {en},
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Peng Cao; Shanli Sun. Lie algebras generated by Jordan operators. Studia Mathematica, Tome 187 (2008) pp. 267-274. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm186-3-5/