论文标题
操作员模块，注射措施和可正态动作的期望较弱
A weak expectation property for operator modules, injectivity and amenable actions
论文作者
论文摘要
我们在完全承包的Banach代数$ a $的情况下，在运营商模块的级别上介绍了弱期望属性（WEP）的等效版本。我们证明了许多一般结果 - 例如，按照适当的$ a $ imentive信封的$ a-wep表征，以及对$ a-wep所暗示的$ a $ a $ a的表征。在$ a = l^1（g）$的情况下，我们在最近的公共汽车工作中恢复了$ g $ - $ c $ -c^*$ - 代数 - echterhoff - willett。当$ a = a（g）$时，我们在傅立叶代数上获得了操作员模块的双重概念。这些双重概念在动态系统的设置中相关，在其中我们表明，当$ m $ imentive a $ w^*$ - 动态系统$（m，g，α）$具有$ m $注射剂时，只有$ m $是$ l^1（g）$ - 当且仅当交叉产品$ g \ bar g \ bar {\ ltimes} m $是$ a $ a（g）时，只有$ l^1（g）$ - IND-INGIVE。类似地，我们表明$ c^*$ - 动力系统$（a，g，α）$ a $ a $ a $ a $ a $ a $ a $ g $ creact在且仅当$ a $具有$ l^1（g）$ - WEP时，并且仅当减少的交叉产品$ g \ ltimes a $ a（g）$ a（g）$ - wep时。
We introduce an equivariant version of the weak expectation property (WEP) at the level of operator modules over completely contractive Banach algebras $A$. We prove a number of general results---for example, a characterization of the $A$-WEP in terms of an appropriate $A$-injective envelope, and also a characterization of those $A$ for which $A$-WEP implies WEP. In the case of $A=L^1(G)$, we recover the $G$-WEP for $G$-$C^*$-algebras in recent work of Buss--Echterhoff--Willett. When $A=A(G)$, we obtain a dual notion for operator modules over the Fourier algebra. These dual notions are related in the setting of dynamical systems, where we show that a $W^*$-dynamical system $(M,G,α)$ with $M$ injective is amenable if and only if $M$ is $L^1(G)$-injective if and only if the crossed product $G\bar{\ltimes}M$ is $A(G)$-injective. Analogously, we show that a $C^*$-dynamical system $(A,G,α)$ with $A$ nuclear and $G$ exact is amenable if and only if $A$ has the $L^1(G)$-WEP if and only if the reduced crossed product $G\ltimes A$ has the $A(G)$-WEP.
