Lie and Jordan ideals in 𝐵(𝑐₀) and 𝐵(𝑙ᵨ)

Förster, K.-H.; Nagy, B.

doi:10.1090/S0002-9939-1993-1123652-6

Lie and Jordan ideals in $B(c_ 0)$ and $B(l_ \rho )$
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by K.-H. Förster and B. Nagy PDF

Proc. Amer. Math. Soc. 117 (1993), 673-677 Request permission

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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