正Herz-Schur乘子与交叉积的逼近性质
Positive Herz-Schur multipliers and approximation properties of crossed products
摘要：
对于$C^*$ -代数$A$和集合$X$，给出了$K(\ell^2(X))\otimes A$上完全正Schur $A$ -乘子的Stinespring型刻画.然后，我们将它们与$C^*$上的完全正的赫兹-舒尔乘子联系起来，$C^*$ -代数交叉积的形式为$A\rtimes_{α,r} G$，其中$G$是一个离散群，其各种版本在早些时候由Anantharaman-Delaroche，Bédos和Conti以及Dong和Ruan考虑过。后者的地图显示实现近似属性，如核或Haagerup属性，为$A\rtimes_{α,r} G$。
英文摘要：
For a $C^*$-algebra $A$ and a set $X$ we give a Stinespring-type characterisation of the completely positive Schur $A$-multipliers on $K(\ell^2(X))\otimes A$. We then relate them to completely positive Herz-Schur multipliers on $C^*$-algebraic crossed products of the form $A\rtimes_{α,r} G$, with $G$ a discrete group, whose various versions were considered earlier by Anantharaman-Delaroche, Bédos and Conti, and Dong and Ruan. The latter maps are shown to implement approximation properties, such as nuclearity or the Haagerup property, for $A\rtimes_{α,r} G$.
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