arXiv subjects

Wenbo Huang

Publications and source records attributed to Wenbo Huang.

20 records · Page 2Linked to original sources

arXiv2016

Characterizations of Jordan mappings on some rings and algebras through zero products

Let $\mathcal{U}=\left[ \begin{array}{cc} \mathcal{A} & \mathcal{M} \mathcal{N}& \mathcal{B} \end{array} \right]$ be a generalized matrix ring, where $\mathcal{A}$ and $\mathcal{B}$ are 2-torsion free. We prove that if $ϕ:\mathcal{U}\rightarrow \mathcal{U}$ is an additive mapping such that $ϕ(U)\circ V+U\circ ϕ(V)=0$ whenever $UV=VU=0,$ then $ϕ=δ+η$, where $δ$ is a Jordan derivation and $η$ is a multiplier. As its applications, we prove that the similar conclusion remains valid on full matrix algebras, unital prime rings with a nontrivial idempotent, unital standard operator algebras, CDCSL algebras and von Neumann algebras.

math.OA↗

arXiv2016

Characterizations of 2-local derivations and local Lie derivations on some algebras

We prove that every 2-local derivation from the algebra $M_n(\mathcal{A})(n>2)$ into its bimodule $M_n(\mathcal{M})$ is a derivation, where $\mathcal{A}$ is a unital Banach algebra and $\mathcal{M}$ is a unital $\mathcal{A}$-bimodule such that each Jordan derivation from $\mathcal{A}$ into $\mathcal{M}$ is an inner derivation, and that every 2-local derivation on a C*-algebra with a faithful traceable representation is a derivation. We also characterize local and 2-local Lie derivations on some algebras such as von Neumann algebras, nest algebras, Jiang-Su algebra and UHF algebras.

math.OA↗