Maps preserving zero Jordan products on Hermitian operators

Mikhail A. Chebotar, Wen-Fong Ke, Pjek Hwee Lee

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)445-452
Number of pages8
JournalIllinois Journal of Mathematics
Volume49
Issue number2
Publication statusPublished - 2005 Jun

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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