Contributions to the theory of C*-correspondences with applications to multivariable dynamics
Contributions to the theory of C*-correspondences with applications to multivariable dynamics
复制标题
对 C* 对应理论的贡献及其在多变量动力学中的应用
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
E. Katsoulis
中科院分区：
文献类型：
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作者：
E. Kakariadis;E. Katsoulis
受张量代数和多变量C*-动力学理论的启发，我们重新审视了C*-对应理论中的两个基本技术，即对非内射C*-对应的“加尾”和对本质Hilbert双模的内射C*-对应的扩张。我们提供了一个非常广泛的计划“添加一个尾巴”的非内射C*-对应，我们的计划包括“尾巴”的Muhly和Tomforde作为一个特例。我们说明了我们的尾巴的多样性和必要性与多变量C*-动力学理论的几个例子。我们还展示了一个透明的图片膨胀的内射C*-对应的一个基本的希尔伯特双模。作为我们的构造的应用，我们证明了多变量动力学理论中的两个结果，扩展了Davidson和Roydor和Peters的结果。我们还讨论了我们的结果的影响的描述的C*-包络的张量代数作为Cuntz-Pimsner代数的相关C*-对应。
Motivated by the theory of tensor algebras and multivariable C*-dynamics, we revisit two fundamental techniques in the theory of C*-correspondences, the "addition of a tail" to a non-injective C*-correspondence and the dilation of an injective C*-correspondence to an essential Hilbert bimodule. We provide a very broad scheme for "adding a tail" to a non-injective C*-correspondence; our scheme includes the "tail" of Muhly and Tomforde as a special case. We illustrate the diversity and necessity of our tails with several examples from the theory of multivariable C*-dynamics. We also exhibit a transparent picture for the dilation of an injective C*-correspondence to an essential Hilbert bimodule. As an application of our constructs, we prove two results in the theory of multivariable dynamics that extend results of Davidson and Roydor and Peters. We also discuss the impact of our results on the description of the C*-envelope of a tensor algebra as the Cuntz-Pimsner algebra of the associated C*-correspondence.