产品系统：一个基于交换子的综述
Product Systems; a Survey with Commutants in View
摘要：
希尔伯特空间的乘积系统（Arveson系统）和希尔伯特模的乘积系统的理论已经达到了这样一种状态，似乎应该休息一下，看看到目前为止已知的是什么，什么是开放的问题。然而，试图给一个近似完整的帐户在视图页是注定要失败的Arveson系统，因为Tsirelson，权力和Liebscher已经发现了他们强大的方法来构建大型类的例子。在这次调查中，我们集中在理论的一部分，也适用于希尔伯特模。这不仅有助于在可能的主题中进行选择，而且还有助于对Arveson系统的情况进行一些新的阐述。通常，对希尔伯特模有效的证明在希尔伯特空间的情况下也会导致更简单的证明。我们着重讨论了最近关于von Neumann对应的交换子的结果所引起的一些问题，这些结果在希尔伯特空间的情况下，解释了B（H）上E_0-半群的Arveson系统和Bhat系统之间的关系.
英文摘要：
The theory of product systems both of Hilbert spaces (Arveson systems) and product systems of Hilbert modules has reached a status where it seems appropriate to rest a moment and to have a look at what is known so far and what are open problems. However, the attempt to give an approximately complete account in view pages is destined to fail already for Arveson systems since Tsirelson, Powers and Liebscher have discovered their powerful methods to construct large classes of examples. In this survey we concentrate on that part of the theory that works also for Hilbert modules. This does not only help to make a selection among the possible topics, but it also helps to shed some new light on the case of Arveson systems. Often, proofs that work for Hilbert modules also lead to simpler proofs in the case of Hilbert spaces. We put emphasis on those aspects that arise from recent results about commutants of von Neumann correspondences, which, in the case of Hilbert spaces, explain the relation between the Arveson system and the Bhat system associated with an E_0--semigroup on B(H).
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