整数群约化交叉积C^*-代数上半范数的下半连续性  

The Lower Semicontinuity of Seminorms on Crossed Product C*-Algebras of Integer Group

作　　者：沈文涛 

机构地区：[1]南京航空航天大学数学学院,江苏 南京

出　　处：《应用数学进展》2024年第6期2943-2951,共9页Advances in Applied Mathematics

摘　　要：紧量子度量空间结构是算子代数领域非常重要的研究内容,既有重要的理论意义,又有广泛的应用前景.本文利用一般的长度函数构造出一类*-半范数。同时,利用约化交叉积C*-代数的共变表示可以构造出另一类*-半范数。通过讨论它们下半连续性,发现其中一类*-半范数是下半连续的,另一类*-半范数与C*-代数的半范数L的下半连续性是等价的。进一步构造出一类与对应的紧量子度量空间紧密相关的*-半范数。Compact quantum metric space structure is a very important research topic in the field of operator algebras. It has great theoretical significance and a wide range of application prospects. In this paper, a class of *-seminorms is constructed by using the general length function. At the same time, another kind of *-seminorms can be constructed by using the covariant representation of reduced cross product algebras. By discussing their lower semicontinuity, we can find that one type of *-seminorms is lower semicontinuous, while the other type of *-seminorms is equivalent to the lower semicontinuity of the seminorm of C*-algebra. Furthermore, we can a class of *-seminorms that is closely related to the corresponding compact quantum metric space.

关 键 词：长度函数 ^*-半范数 下半连续性 

分 类 号：O17[理学—数学]