CONDITIONAL EXPECTATIONS IN VONNEUMANN-ALGEBRAS AND A THEOREM OF TAKESAKI
CONDITIONAL EXPECTATIONS IN VONNEUMANN-ALGEBRAS AND A THEOREM OF TAKESAKI
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DOI：
10.1016/0022-1236(82)90022-2
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发表时间：
1982-01-01
影响因子：
1.7
通讯作者：
CECCHINI, C
中科院分区：
文献类型：
--
作者：
ACCARDI, L;CECCHINI, C
条件期望在经典概率论中起着重要的作用。在冯诺依曼代数的一般上下文中，它们被冯诺依曼隐式地使用[41，Chap. [14][15][16][17][18]中村和Turumaru [27]和Umegaki [36-391]在von Neumann（或C*-）代数的框架中引入了条件期望概念的公理化定义，并建立了这些对象的许多性质，特别是在具有有限迹的von Neumann代数的背景下。他们的出发点是Moy [26]给出的经典条件期望作为可测函数空间上的算子的特征。Tomiyama证明[33]，在上述作者的意义下，条件期望可以被刻画为C*-代数中的范数一投影。范一投影在冯诺依曼代数分类问题中的重要性被Hakeda和Tomiyama [23]所认识，随后对这一论点的研究证实了这些对象的有用性。这条思路最终在康纳斯的基本工作[121]，其中近似有限冯
Conditional expectations play an important role in classical probability theory. In the general context of von Neumann algebras they were impliciteiy used by von Neumann [41, Chap. II] and by Dixmier [14]. Nakamura and Turumaru [27] and Umegaki [36-391 introduced an axiomatic definition of the concept of conditional expectation in the framework of von Neumann (or C*-) algebras and established many properties of these objects especially in the context of von Neumann algebras with a finite trace. Their starting point was the characterization, given by Moy [26], of the classical conditional expectations as operators on spaces of measurable functions. Tomiyama showed [33] that conditional expectations, in the sense of the above mentioned authors, can be characterized as norm one projection in C*-algebras. The importance of norm one projection in the classification problem of von Neumann algebras was recognized by Hakeda and Tomiyama [23] and subsequent research on this argument confirmed the usefulness of these objects. This line of thought culminated in the fundamental work of Connes [121 in which approximately finite von