C*-代数中具有翻转作用的三个酉元旋转关系的稳定性——全部扰动的情况
Stability of Rotation Relations of Three Unitaries with the Flip Action in C*-Algebras—Case of Total Perturbation
DOI: 10.12677/pm.2024.146240, PDF,    国家自然科学基金支持
作者: 吴慧慧：浙江师范大学数学科学学院，浙江 金华；花家杰：嘉兴大学数据科学学院，浙江 嘉兴
关键词: C*-代数；稳定性；旋转关系；翻转作用；C*-Algebra； Stability； Rotation Relation； Flip Action
摘要: 在本文中我们证明了若Θ=(θjk)是3×3完全无理实斜对称矩阵，其中θjk∈[0,1)，j,k=1,2,3，那么对于任意的ε>0，存在δ>0满足以下结论：在任何具有消去性质、严格比较性质、非空迹态空间、有单位元的C*-代数A中，任意四个酉元u1,u2,u3,w∈A，如果并且u1 ,u2 ,u3 ,w满足一定的迹条件，那么存在四个酉元u~1，u~2，u~3，w~∈A使得
Abstract: We show that ifΘ=(θjk)is a3×3totally irrational real skew-symmetric matrix, whereθjk∈[0,1)forj,k=1,2,3, then for anyε>0, there existsδ>0satisfying the following: for any unital C*-algebra A with the cancellation property, strict comparison and nonempty tracial state space, any four unitariesu1,u2,u3,w∈Asuch that and u1 ,u2 ,u3 ,w satisfy some trace conditions, there exists a 4-tuple of unitaries u~1，u~2，u~3，w~∈A such that
文章引用：吴慧慧, 花家杰. C*-代数中具有翻转作用的三个酉元旋转关系的稳定性——全部扰动的情况[J]. 理论数学, 2024, 14(6): 193-210. https://doi.org/10.12677/pm.2024.146240

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