Unit Vectors, Morita Equivalence and Endomorphisms
Unit Vectors, Morita Equivalence and Endomorphisms
复制标题
单位向量、森田等价和自同态
DOI：
10.2977/prims/1241553127
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发表时间：
2004
影响因子：
1.2
通讯作者：
Michael Skeide
中科院分区：
文献类型：
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作者：
Michael Skeide
我们解决了对应理论中的两个问题，这两个问题对产品系统理论具有重要意义。第一个问题是，是否每个对应关系都是（通过表示论）与希尔伯特模上所有可邻算子的代数的单位自同态相关联的对应关系。第二个问题是每个对应关系是否都允许希尔伯特空间上的非简并忠实表示。我们还解决了对应表示的扩展问题，并为 W* 代数表示理论中的几个众所周知的陈述提供了新的有效证明。
We solve two problems in the theory of correspondences that have important implications in the theory of product systems. The first problem is the question whether every correspondence is the correspondence associated (by the representation theory) with a unital endomorphism of the algebra of all adjointable operators on a Hilbert module. The second problem is the question whether every correspondence allows for a nondegenerate faithful representation on a Hilbert space. We also solve an extension problem for representations of correspondences and we provide new efficient proofs of several well-known statements in the theory of representations of W ∗ –algebras.