arXiv subjects
Publications and source records attributed to Wu Jing.
The main purpose of this article is to show that every commuting Jordan derivation on triangular rings (unital or not) is identically zero. Using this result, we prove that if $\mathcal{A}$ is a 2-torsion free ring such that it is either semiprime or satisfies Condition (P), then every commuting Jordan derivation from $\mathcal{A}$ into itself, under certain conditions, is identically zero.
In this note we prove that elementary maps on triangular algebras are automically additive.
We prove that every multiplicative bijective map, Jordan bijective map, and Jordan triple bijective map from a triangular algebra onto any ring is automatically additive.
In this short note we prove that every Jordan derivation of triangular algebras is a derivation.
We prove that Jordan triple elementary surjective maps on unital rings containing a nontrivial idempotent are automatically additive.
We prove that Jordan elementary surjective maps on rings are automatically additive.
We investigate the structured frames for Hilbert $C^{*}$-modules. In the case that the underlying $C^{*}$-algebra is a commutative $W^*$-algebra, we prove that the set of the Parseval frame generators for a unitary operator group can be parameterized by the set of all the unitary operators in the double commutant of the group. Similar result holds for the set of all the general frame generators where the unitary operators are replaced by invertible and adjointable operators. Consequently, the set of all the Parseval frame generators is path-connected. We also obtain the existence and uniqueness results for the best Parseval multi-frame approximations for multi-frame generators of unitary operator groups on Hilbert $C^*$-modules when the underlying $C^{*}$-algebra is commutative.