| 非单C~*-代数α-比较性的等价刻画 |
| |
| 引用本文： | 梁月亮,方小春,范庆斋.非单C~*-代数α-比较性的等价刻画[J].数学学报,2017,60(4):705-712. |
| |
| 作者姓名： | 梁月亮 方小春 范庆斋 |
| |
| 作者单位： | 1. 中北大学理学院 太原 030051;
2. 同济大学数学系 上海 200092;
3. 上海海事大学文理学院数学系 上海 201306 |
| |
| 基金项目： | 国家自然科学基金（11371279）；中北大学校青年基金；山西省回国留学人员科研资助项目 |
| |
| 摘 要： | 给出非单C~*-代数α-比较性的等价刻画:当每个τ∈QT(■H)均为忠实时,■具有α-比较性,当且仅当对于任意的〈a〉,〈b〉∈Cu(■)且∝,若α·d_τ(a)≤在Cu(■)中成立;一般地,当QT(■H)≠Φ时,■具有α-比较性,当且仅当对于任意的,∈Cu(■),若存在η>0,使得d_τ(α)≤(α~(-1)-η)d_τ(b)(_τ∈QT(■H)),则≤在Cu(■)中成立.
|
| 关 键 词： | α-比较性 Cuntz半群 下半连续的拟迹 |
Equivalent Characterizations for the α-comparison Property of Non-simple C*-algebras |
| |
| Yue Liang LIANG,Xiao Chun FANG,Qing Zhai FAN.Equivalent Characterizations for the α-comparison Property of Non-simple C*-algebras[J].Acta Mathematica Sinica,2017,60(4):705-712. |
| |
| Authors: | Yue Liang LIANG Xiao Chun FANG Qing Zhai FAN |
| |
| Institution: | 1. School of Sciences, North University of China, Taiyuan 030051, P. R. China;
2. Department of Mathematics, Tongji University, Shanghai 200092, P. R. China;
3. College of Arts and Sciences, Shanghai Maritime University, Shanghai 201306, P. R. China |
| |
| Abstract: | This note is to give such characterizations of the α-comparison property for non-simple C*-algebras:when each τ∈QT(A?K) is faithful,A has the α-comparison property,if and only if,for any 〈a〉,〈b〉∈Cu (A) with 〈a〉∝〈b〉,α·dτ(a)0 such that dτ(a)≤(α-1-η)dτ(b)(?τ,∈QT(A?K)),then 〈a〉 ≤ 〈b〉inCu (A). |
| |
| Keywords: | α-comparison property Cuntz semigroup lower semi-continuous quasitrace |
| 本文献已被 CNKI 等数据库收录！ |
| 点击此处可从《数学学报》浏览原始摘要信息 |
| 点击此处可从《数学学报》下载免费的PDF全文 |
|
