论文标题
双操作员空间的交叉产品和具有近似特性的组的表征
Crossed products of dual operator spaces and a characterization of groups with the approximation property
论文作者
论文摘要
令$ g $为本地紧凑型组。我们在双操作员空间和相关的交叉产品中研究$ l^{\ infty}（g）$编码和$ l（g）$编码的类别。事实证明，每个$ l^{\ infty}（g）$ comodule是非分级和饱和的，而当每个$ l（g）$ -OBODULE都不是当每个$ l（g）$ compoule时，并且仅当$ g $具有haagerup和kraus [14]时，只有且仅当$ g $就具有近似属性时，只有每一个$ l（g）$ comcomodule均为饱和。这使我们可以将已知结果从冯·诺伊曼代数（例如takeaki二元性和digernes-takesaki定理）的二重性理论扩展到最新的双操作员空间的交叉产物理论。作为应用，我们从相关的交叉产品方面获得了具有近似特性的组的表征，这些杂交产品改善了Crann和Neufang [9]的最新结果，并且我们概括了Anoussis，Katavolos和Todorov [2]的定理，从而提供了较低的技术证明。此外，这种方法为作者在[2]中提出的问题提供了答案。
Let $ G $ be a locally compact group. We study the categories of $ L^{\infty}(G) $-comodules and $ L(G) $-comodules in the setting of dual operator spaces and the associated crossed products. It is proved that every $ L^{\infty}(G) $-comodule is non-degenerate and saturated, whereas every $ L(G) $-comodule is non-degenerate if and only if every $ L(G) $-comodule is saturated if and only if $ G $ has the approximation property in the sense of Haagerup and Kraus [14]. This allows us to extend known results from the duality theory of crossed products of von Neumann algebras (such as Takesaki-duality and the Digernes-Takesaki theorem) to the recent theory of crossed products of dual operator spaces. As applications, we obtain a characterization of groups with the approximation property in terms of the related crossed products improving a recent result of Crann and Neufang [9] and we generalize a theorem of Anoussis, Katavolos and Todorov [2] providing a less technical proof of it. Furthermore, this approach provides an answer to a question raised by the authors in [2].
