Let H be a separable complex Hilbert space and B3́(H) the Jordan algebra of all Hermitian operators on H. Let θ: B3 (H) → B3(H) be a surjective ℝ-linear map which is continuous in the strong operator topology such that θ(x)θ(y)+θ(y)θ(x) = 0 for all x,y ∈ Bs(H) with xy + yx = 0. We show that θ(x) = Xλuxu* for all x ∈ Bs(H), where λ is a nonzero real number and u is a unitary or anti-unitary operator on H.
|Number of pages||8|
|Journal||Illinois Journal of Mathematics|
|Publication status||Published - 2005 Jun|
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