Lie algebras generated by Jordan operators

Peng Cao, and Shanli Sun. "Lie algebras generated by Jordan operators." Studia Mathematica 186.3 (2008): 267-274. <http://eudml.org/doc/284512>.

@article{PengCao2008,
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 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.},
author = {Peng Cao, Shanli Sun},
journal = {Studia Mathematica},
keywords = {normal-equivalent operators; Engel Lie algebras; Jordan operators},
language = {eng},
number = {3},
pages = {267-274},
title = {Lie algebras generated by Jordan operators},
url = {http://eudml.org/doc/284512},
volume = {186},
year = {2008},
}

TY - JOUR
AU - Peng Cao
AU - Shanli Sun
TI - Lie algebras generated by Jordan operators
JO - Studia Mathematica
PY - 2008
VL - 186
IS - 3
SP - 267
EP - 274
AB - 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.
LA - eng
KW - normal-equivalent operators; Engel Lie algebras; Jordan operators
UR - http://eudml.org/doc/284512
ER -