A+ CATEGORY SCIENTIFIC UNIT

Lie algebras generated by Jordan operators

Volume 186 / 2008

Peng Cao, Shanli Sun 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.

Authors

  • 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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