乘积系的可加单位
Additive units of product systems
摘要：
我们引入的概念，添加剂的单位，或“添加剂”，一个点的Arveson系统，并通过几个应用程序证明其实用性。所谓尖的Arveson系统，我们指的是具有固定归一化参考单位的空间Arveson系统。我们表明，addits形成一个希尔伯特空间的余维一个子空间的“根”是同构的指标空间的Arveson系统，和addits生成的I型部分的Arveson系统。因此加法的希尔伯特空间的同构类与参考单位无关。一个点包含系统的加法被证明是在自然的对应与生成的点产品系统的加法。利用加法和根发展了合并积理论，给出了点Arveson系统合并的显式公式，并给出了其独立于特定参考单位的新证明. (This独立性证明了空间Arveson系统的术语“空间产品”的合理性）。最后介绍了Arveson系统的包含子系统的集群建设，我们证明了其对应的康托-Bendixson导数的随机闭集方法的范围内的产品系统由于Tsirelson和Liebscher的行动。
英文摘要：
We introduce the notion of additive units, or `addits', of a pointed Arveson system, and demonstrate their usefulness through several applications. By a pointed Arveson system we mean a spatial Arveson system with a fixed normalised reference unit. We show that the addits form a Hilbert space whose codimension-one subspace of `roots' is isomorphic to the index space of the Arveson system, and that the addits generate the type I part of the Arveson system. Consequently the isomorphism class of the Hilbert space of addits is independent of the reference unit. The addits of a pointed inclusion system are shown to be in natural correspondence with the addits of the generated pointed product system. The theory of amalgamated products is developed using addits and roots, and an explicit formula for the amalgamation of pointed Arveson systems is given, providing a new proof of its independence of the particular reference units. (This independence justifies the terminology `spatial product' of spatial Arveson systems). Finally a cluster construction for inclusion subsystems of an Arveson system is introduced and we demonstrate its correspondence with the action of the Cantor--Bendixson derivative in the context of the random closed set approach to product systems due to Tsirelson and Liebscher.
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