论文标题
有限陈述，本地提升属性和操作员模块的局部近似属性
Finite presentation, the local lifting property, and local approximation properties of operator modules
论文作者
论文摘要
我们介绍了有限陈述和共同享用性的概念，这些概念是对完全承诺的Banach代数的有限量化模块的定性和定量类似物。通过这些概念，我们通过引入局部提升性质，核性和半差异性的类似物来开始开发当地的操作员模块理论。对于大量的运算符模块，我们证明本地提升属性等于平坦度，从而推广了Kye和Ruan的操作员空间的结果。我们将应用于抽象的谐波分析，其中，对于本地紧凑的量子组$ \ mathbb {g} $，我们表明$ l^1（\ Mathbb {g}）$ - $ \ Mathrm {luc {luc {luc {luc mathbb {g Mathbb {g}）的核能$ l^\ infty（\ mathbb {g}）$均等效于$ \ mathbb {g} $的共同性。我们建立了$ a（g）$ - 注射率的$ g \ bar {\ ltimes} m $，$ a（g）$ - $ g \ bar {\ ltimes} m $的半差异性，以及$ w^*$ - $ w^*$ - 动态系统$（m，g，ltimes $ m，g，α）$，$ m $ m $ m $ indective。我们以未来方向的评论结束。
We introduce notions of finite presentation and co-exactness which serve as qualitative and quantitative analogues of finite-dimensionality for operator modules over completely contractive Banach algebras. With these notions we begin the development of a local theory of operator modules by introducing analogues of the local lifting property, nuclearity, and semi-discreteness. For a large class of operator modules we prove that the local lifting property is equivalent to flatness, generalizing the operator space result of Kye and Ruan. We pursue applications to abstract harmonic analysis, where, for a locally compact quantum group $\mathbb{G}$, we show that $L^1(\mathbb{G})$-nuclearity of $\mathrm{LUC}(\mathbb{G})$ and $L^1(\mathbb{G})$-semi-discreteness of $L^\infty(\mathbb{G})$ are both equivalent to co-amenability of $\mathbb{G}$. We establish the equivalence between $A(G)$-injectivity of $G\bar{\ltimes}M$, $A(G)$-semi-discreteness of $G\bar{\ltimes} M$, and amenability of $W^*$-dynamical systems $(M,G,α)$ with $M$ injective. We end with remarks on future directions.
