特征函数、提升和模
Characteristic Functions, Liftings and Modules
摘要：
我们回顾了如何将Beurling型定理的一些多解析内函数与G. Popescu的工作之后的行压缩相关联。受弱马尔可夫伸缩的结果的启发，我们定义了一个特征函数的概念遍历和共等距行压缩与一维不变子空间的伴随。我们的特征函数是一个完整的酉不变的元组。此后，我们将特征函数的分析扩展到行压缩的压缩提升。我们应用我们的理论完全积极的地图，并探讨应用程序的不动点集的完全积极的地图相关的一个subisometric提升。在最后两章中，我们考虑了约束行压缩和一些模结构。
英文摘要：
We review how some multianalytic inner functions of the Beurling type theorem are associated to row contractions following works of G.Popescu. Motivated by a result on weak Markov dilations, we define a notion of characteristic function for ergodic and coisometric row contractions with a one-dimensional invariant subspace for the adjoints. Our characteristic function is a complete unitary invariant for such tuples. Thereafter we extend the analysis of characteristic functions to contractive liftings of row contractions. We apply our theory to completely positive maps and explore applications to fixed point sets of completely positive maps related to each other by a subisometric lifting. In the last two chapter we consider constrained row contractions and some module structures in this context.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
