Lie and Jordan ideals of operators on Hilbert space
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- by C. K. Fong, C. R. Miers and A. R. Sourour PDF
- Proc. Amer. Math. Soc. 84 (1982), 516-520 Request permission
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
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Additional Information
- © Copyright 1982 American Mathematical Society
- 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