2018/03/06 by Guangyu An, Jun He, An, Guangyu +1 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #math.OA
paper · pdf · doi:10.48550/arxiv.1803.02050
arxiv created 2018/03/06 · openalex publication_date 2018/03/06 · arxiv updated 2018/03/07 · openalex created_date 2018/03/29 · openalex updated_date 2026/07/28
We prove that if \mathcal M is a properly infinite von Neumann algebra and LS(\mathcal M) is the local measurable operator algebra affiliated with \mathcal M, then every Jordan derivation from LS(\mathcal M) into itself is continuous with respect to the local measure topology t(\mathcal M). We construct an extension of a Jordan derivation from \mathcal M into LS(\mathcal M) up to a Jordan derivation from LS(\mathcal M) into itself. Moreover, we prove that if \mathcal M is a properly von Neumann algebra and \mathcal A is a subalgebra of LS(\mathcal M) such that \mathcal M⊂\mathcal A, then every Jordan derivation from \mathcal A into LS(\mathcal M) is continuous with respect to the local measure topology t(\mathcal M).