2018/05/05 by Wen-Hui Lin, Lin, Wenhui · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1805.02037
openalex publication_date 2018/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let H be a complex Hilbert space, B(H) be the algebra of all bounded linear operators on H and A ⊆ B(H) be a von Neumann algebra without central summands of type I1. For arbitrary elements A, B∈ A, one can define their ∗-Jordan product in the sense of A\diamond B = AB+BA^∗. Let pn(x1,x2,⋯,xn) be the polynomial defined by n indeterminates x1, ⋯, xn and their ∗-Jordan products. In this article, it is shown that a mapping δ: A \longrightarrow B(H) satisfies the condition δ(pn(A1, A2,⋯, An))=∑k=1n pn(A1,⋯, Ak-1, δ(Ak), Ak+1,⋯, An) for all A1, A2,⋯, An ∈ A if and only if δ is an additive ∗-derivation.