简单迹极限的基本可比性

Fundamental Comparison of Simple Tracial Limit

引进了简单迹极限的相关概念,简单介绍了与C*代数SP性质密切相关的F性质,并且得到了非基本的单的具有SP性质的C*代数具有F性质.在此基础上得出简单迹极限的基本可比性.其主要结果:设A为具有F性质的带单位元1的C*代数,且A的迹态空间T(A)为非空集,如果对每个自然数n,An具有基本可比性,则An的简单迹极限A也具有基本可比性。

An introduction to the definition of the simple tracial limit of C^＊-algebra is first made in this paper. Then, the relationship between the property （SP） and the property F of C^＊-algebra A is studied. A perfect conclusion is obtained on fundamental comparison of simple tracial limit： Let A be a unital C^＊ -algebra with the property F the tracial space of A nonempty, if A, has the property of fundamental comparison for each natural number n, then, simple tracial limit of An has the property of fundamental comparison.