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Proceedings of the American Mathematical Society

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Lie and Jordan ideals in $ B(c\sb 0)$ and $ B(l\sb \rho)$


Authors: K.-H. Förster and B. Nagy
Journal: Proc. Amer. Math. Soc. 117 (1993), 673-677
MSC: Primary 47D50; Secondary 46L70, 47B37, 47D30
DOI: https://doi.org/10.1090/S0002-9939-1993-1123652-6
MathSciNet review: 1123652
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Abstract: It is shown that ideals with respect to the canonical Lie (commutator) product in these algebras are exactly the linear manifolds that contain the images of their elements under the action of inner automorphisms induced by invertible spectral operators of scalar type. Jordan ideals in these algebras are identical with two-sided associative ideals and are also applied to a characterization of Lie ideals.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1123652-6
Keywords: Associative, Lie and Jordan ideals, $ B({c_0}),\;B({l_\rho })$, spectral operator of scalar type, commutator
Article copyright: © Copyright 1993 American Mathematical Society