Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Lie and Jordan ideals of operators on Hilbert space


Authors: C. K. Fong, C. R. Miers and A. R. Sourour
Journal: Proc. Amer. Math. Soc. 84 (1982), 516-520
MSC: Primary 47D25
DOI: https://doi.org/10.1090/S0002-9939-1982-0643740-0
MathSciNet review: 643740
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A linear manifold $\mathfrak {L}$ in $\mathfrak {B}(\mathfrak {H})$ is a Lie ideal in $\mathfrak {B}(\mathfrak {H})$ if and only if there is an associative ideal $\mathfrak {J}$ such that $[\mathfrak {J},\mathfrak {B}(\mathfrak {H})] \subseteq \mathfrak {L} \subseteq \mathfrak {J} + {\mathbf {C}}I$. Also $\mathfrak {L}$ is a Lie ideal if and only if it contains the unitary orbit of every operator in it. On the other hand, a subset of $\mathfrak {B}(\mathfrak {H})$ is a Jordan ideal if and only if it is an associative ideal.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47D25

Retrieve articles in all journals with MSC: 47D25


Additional Information

Article copyright: © Copyright 1982 American Mathematical Society