J. Zhang
College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi, 710062, P.R. China.
[ 1 ] - Dilations for $C^ast$-dynamical systems with abelian groups on Hilbert $C^ast$-modules
In this paper we investigate the dilations of completely positive definite representations of \(C^\ast\)-dynamical systems with abelian groups on Hilbert \(C^\ast\)-modules. We show that if \((\mathcal{A}, G,\alpha)\) is a \(C^\ast\)-dynamical system with \(G\) an abelian group, then every completely positive definite covariant representation \((\pi,\varphi,E)\) of \((\mathcal{A}, G,\alpha)\) on …
[ 2 ] - Nonlinear $*$-Lie higher derivations on factor von Neumann algebras
Let $\mathcal M$ be a factor von Neumann algebra. It is shown that every nonlinear $*$-Lie higher derivation $D={\phi_{n}}_{n\in\mathbb{N}}$ on $\mathcal M$ is additive. In particular, if $\mathcal M$ is infinite type $I$ factor, a concrete characterization of $D$ is given.