2018/03/06 by Guangyu An, Jun He, An, Guangyu +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1803.02046
openalex publication_date 2018/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathcal R be a ring, M be a \mathcal R-bimodule and m,n be two fixed nonnegative integers with m+n≠0. An additive mapping δ from \mathcal R into M is called an (m,n)-Jordan derivation if (m+n)δ(A2)=2mAδ(A)+2nδ(A)A for every A in \mathcal R. In this paper, we prove that every (m,n)-Jordan derivation from a C*-algebra into its Banach bimodule is zero. An additive mapping δ from \mathcal R into M is called a (m,n)-Jordan derivable mapping at W in \mathcal R if (m+n)δ(AB+BA)=2mδ(A)B+2mδ(B)A+2nAδ(B)+2nBδ(A) for each A and B in \mathcal R with AB=BA=W. We prove that if M is a unital \mathcal A-bimodule with a left (right) separating set generated algebraically by all idempotents in \mathcal A, then every (m,n)-Jordan derivable mapping at zero from \mathcal A into M is identical with zero. We also show that if A and B are two unital algebras, M is a faithful unital (A,B)-bimodule and U=[A · amp;M
N · amp; B] is a generalized matrix algebra, then every (m,n)-Jordan derivable mapping at zero from U into itself is equal to zero.